RD SHARMA Solutions for Class 12-science Maths Chapter 20 - Definite Integrals

Chapter 20 - Definite Integrals Exercise Ex. 20.1

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 34
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 34
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 37
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 37
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 40
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 40
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 41
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 41
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 42
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 44
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 44
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 45
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 46
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 46
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 47
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 47
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 49
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 49
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 50
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 50
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 52
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 52
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 54
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 54
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 55

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Let cosx =u , Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 56
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 56
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Given :

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 63

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

We know , By reduction formula 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

For n=2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

For n=4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Note: Answer given at back is incorrect.

Question 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 64

Using Integration By parts

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 65

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 65

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Note: Answer given in the book is incorrect. 

Question 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 =(1/4)log(2e)

 

Chapter 20 - Definite Integrals Exercise Ex. 20.2

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 24

Using Integration By parts

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 27

Evaluate Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 30

?Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 33
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 33
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 34
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 34
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 35
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 35
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 37
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 37
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 42
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 42
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 44
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 45
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 45
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 46
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 46
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 47
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Solution 47
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 58

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Chapter 20 - Definite Integrals Exercise Ex. 20.3

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 5

2x+3 is positive for x>-1.5 . Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17

Evaluate the integral Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

For

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Using Integration By parts

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

For

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Using Integration By parts

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 27

[x]=0 for 0 < x

and [x]=1 for 1< x < 2

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 26

Evaluate the following integrals:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals


Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

NOTE: Answer not matching with back answer.

Chapter 20 - Definite Integrals Exercise Ex. 20.4A

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 1

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then also

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 2

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 3

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 4

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 5

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

We know

 

If f(x) is even

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If f(x) is odd

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Here

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

f(x) is even, hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Note: Answer given in the book is incorrect.

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 6

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 7

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 8

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Note: Answer given in the book is incorrect. 

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If f(x) is even

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

If f(x) is odd

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Here

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals is odd and

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals is even. Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Chapter 20 - Definite Integrals Exercise Ex. 20.4B

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 3

BRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Now

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Let cosx=t

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 34

Evaluate the integral Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 38

We know

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Also here

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

So

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Hence

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Chapter 20 - Definite Integrals Exercise Ex. 20RE

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21

Evaluate the integral Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 65

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 65

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 68

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 68

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 69

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 69

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Chapter 20 - Definite Integrals Exercise Ex. 20.5

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals
Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Chapter 20 - Definite Integrals Exercise MCQ

Question 1

Mark the correct alternative in each of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p/2

(b) p/4

(c) p/6

(d) p/8

Solution 1

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) 1/2

(c) 2

(d) 3/2

Solution 2

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 3

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) 2

(c) 8

(d) 4

 

Solution 4

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Note: Answer not matching with back answer.

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) p/2

(c) p/4

(d) None of these

 

Solution 5

Correct option:(c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) Log 2-1

(b) Log 2

(c) Log 4-1

(d) -log 2

 

Solution 6

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 2

(b) 1

(c) p/4

(d) p2/8

 

Solution 7

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 8

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 9

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Note: Answer not matching with back answer.

Question 11

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 11

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p/3

(b) p/6

(c) p/12

(d) p/2

 

Solution 12

Correct option:(c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 13

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 1

(b) e-1

(c) e+1

(d) 0

 

Solution 14

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 15

Correct option:(a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 16

Correct option:(a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 17

Correct option:(b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 1

(b) 2

(c) -1

(d) -2

 

Solution 18

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 19

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 1

(b) e-1

(c) 0

(d) -1

 

Solution 20

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 21

Correct option:(b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 4a2 

(b) 0

(c) 2a2 

(d) None of these

 

Solution 22

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 23

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 24

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) -2

(b) 2

(c) 0

(d) 4

 

Solution 25

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 26

Correct option:(c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 27

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 28

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Note: Question is modified.

 

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 4

(b) 2

(c) -2

(d) 0

 

Solution 30

Correct option:(a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) 1

(c) p/2

(d) p/4

 

Solution 31

Correct option:(d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p 

(b) p/2

(c) p/3

(d) p/4

 

Solution 32

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) p 

(c) p/2

(d) p/4

 

Solution 33

Correct option:(c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Note: Answer not matching with back answer.

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p/4

(b) p/2

(c) p 

(d) 1

 

Solution 34

Correct option:(d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Note: Answer not matching with back answer.

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p 

(b) p/2

(c) 0

(d) 2p 

 

Solution 35

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p/4

(b) p/8

(c) p/2

(d) 0

 

Solution 36

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) p In 2

(b) -p In 2

(c) 0

(d) Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 37

Correct option:(d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

NOTE: Answer is not matching with back answer. 

 

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 38

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

 

Solution 39

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 1

(b) 0

(c) -1

(d) p/4

 

Solution 40

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 2

(b) Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(c) 0

(d) -2

Solution 41

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

 

Question 42

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

(a) 0

(b) 2

(c) p 

(d) 1

Solution 42

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals 

Chapter 20 - Definite Integrals Exercise Ex. 20VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 28 n

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 28 n

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Note: The lower limit is incorrect in textbook. Consider the lower limit as '0'.

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Definite Integrals