# RD SHARMA Solutions for Class 12-science Maths Chapter 21 - Areas of Bounded Regions

## Chapter 21 - Areas of bounded regions Exercise Ex. 21.1

Thus, Required area = square units

Sketch
the region {(x, y):9x^{2} + 4y^{2} = 36} and find the area
enclosed by it, using integration.

9x^{2} + 4y^{2} =
36

Area of Sector OABCO =

Area of the whole figure = 4 × Ar. D OABCO

= 6p sq. units

What dose this integral represent on the graph?.

and evaluate the area of the region under the curve and above the x-axis.

Find the area of the minor segment of the circle x^{2} + y^{2} = a^{2} cut off by the line x =

Find the area of the region bounded by the curve x = at^{2}, y = 2at between the ordinates corresponding t = 1 and t = 2.

Find the area enclosed by the curve x = 3 cost,

y = 2 sin t.

## Chapter 21 - Areas of Bounded Regions Exercise Ex. 21.2

Find
the area of the region bounded by x^{2} = 4ay and its latusrectum.

Find
the area of the region bounded by x^{2} + 16y = 0 and its latusrectum.

Find the area of the region bounded by the curve ay^{2} = x^{3}, the y-axis and the lines y = a and y = 2a.

## Chapter 21 - Areas of Bounded Regions Exercise Ex. 21.3

Find
the area of the region common to the parabolas 4y^{2} = 9x and 3x^{2}
= 16y.

Find the area of the region between the circles x^{2} + y^{2} = 4 and (x - 2)^{2} + y^{2} = 4.

Using Integration, find the area of the region bounded by the triangle whose vertices are (- 1, 2), (1, 5) and (3, 4).

Equation of side AB,

Equation of side BC,

Equation of side AC,

Area of required region

= Area of EABFE + Area of BFGCB - Area of AEGCA

Calculate the area of the region bounded by the parabolas y^{2} = 6x and x^{2} = 6y.

Find the area of the region bounded by y =, x = 2y + 3 in the first quadrant and x-axis.

Find the area of the bounded by y =and y = x.

Find the area enclosed by the curve y = -x^{2} and the straight line x + y + 2 = 0.

Using the method of integration, find the area of the region bounded by the following lines: 3x - y - 3 = 0,

2x + y - 12 = 0, x - 2y - 1 = 0.

Find the area of the region enclosed by the parabola

x^{2} = y and the line y = x + 2.

## Chapter 21 - Areas of Bounded Regions Exercise Ex. 21.4

Find the area of the region between the parabola x = 4y - y^{2} and the line x = 2y - 3.

Find the area bounded by the parabola x = 8 + 2y - y^{2}; the y-axis and the lines y = -1 and y = 3.

Find the area bounded by the parabola y^{2} = 4x and the line

y = 2x - 4.

i. By using horizontal strips

ii. By using vertical strips

Find the area of the region bounded the parabola y^{2} = 2x and straight line x - y = 4.

## Chapter 21 - Areas of Bounded Regions Exercise MCQ

a. 1/ 2

b. 1

c. -1

d. 2

Correct option: (b)

The area included between the parabolas y^{2}=4x and x^{2} = 4y is (in square units)

a. 4/3

b. 1/3

c. 16/3

d. 8/3

Correct option: (c)

The area bounded by the curve y= log_{e} x and x-axis and the straight line x =e is

- e. sq. units
- 1 sq. units

Correct option: (b)

The area bounded by y=2-x^{2} and x + y =0 is

Correct option: (b)

The area bounded by the parabola x =4 -y^{2} and y-axis, in square units, is

Correct option: (b)

If A_{n }be the area bounded by the curve y = (tan x)^{n} and the lines x = 0, y =0 and x =π /4, then for x > 2

Correct option: (a)

The area of the region formed by x^{2}+y^{2}-6x-4y+12 ≤ x and x ≤ 5/2 is

Correct option: (c)

a. 2

b. 1

c. 4

d. None of these

Correct option: (a)

The area of the region bounded by the parabola (y-2)^{2} =x-1 , the tangent to it at the point with the ordinate 3 and the x-axis is

- 3
- 6
- 7
- None of these

Correct option: (d)

NOTE: Answer not matching with back answer.

The area bounded by the curves y = sin x between the ordinates x =0 , x =π and the x-axis is

- 2 sq. units
- 4 sq. units
- 3 sq. units
- 1 sq. units

Correct option: (a)

The area bounded by the parabola y^{2} = 4ax and x^{2} = 4 ay is

Correct option: (b)

The area bounded by the curve y=x^{4}-2x^{3}+x^{2}+3 with x-axis and ordinates corresponding to the minima of y is

Correct option: (b)

The area bounded by the parabola y^{2}=4ax, latus rectum and x-axis is

Correct option: (b)

Correct option: (c)

NOTE: Answer not matching with back answer.

The area common to the parabola y = 2x^{2 }and y=x^{2}+4 is

Correct option: (c)

The area of the region bounded by the parabola y=x^{2}+1 and the straight line x + y =3 is give by

Correct option: (d)

The ratio of the areas between the curves y= cos x and y = cos 2x and x-axis from x =0 to x = π/3 is

- 1:2
- 2:1
- None of these

Correct options: (d)

NOTE: Answer not matching with back answer.

The area between x-axis and curve y = cos x when 0 ≤ x ≤ 2 π is

- 0
- 2
- 3
- 4

Correct option: (d)

Area bounded by parabola y^{2}=x and staright line 2y = x is

- 4/3
- 1
- 2/3
- 1/3

Correct option: (a)

NOTE: Options are modified.

The area bounded by the curve y = 4x-x^{2} and x-axis is

Correct option: (c)

Area enclosed between the curve y^{2}(2a-x)=x^{3} and the line x =2a above x-axis is

Correct option: (b)

The area of the region (in square units)bounded by the curve x^{2}=4y, line x =2 and x-axis is

- 1
- 2/3
- 4/3
- 8/3

Correct option: (b)

The area bounded by the curve y=f (x), x-axis, and the ordinates x =1 and x=b is (b-1) sin (3b+4). Then, f (x) is

- (x-1) cos (3x+4)
- Sin (3x+4)
- Sin (3x+4)+3(x-1)cos (3x+4)
- None of these

Correct option: (c)

The area bounded by the curve y^{2} =8x and x^{2}=8y is

NOTE: Answer is not matching with back answer.

The area bounded by the parabola y^{2}=8x, the x-axis, and the latus rectum is

Correct option: (a)

NOTE: Answer is not matching with back answer.

Area bounded by the curve y=x^{3}, the x-axis and the ordinates x =-2 and x =1 is

Correct option: (d)

The area bounded by the curve y = x |x| and the ordinates x =-1 and x = 1 is given by

Correct option: (c)

Correct option:(b)

The area of the circle x^{2} +y^{2}=16 interior to the parabola y^{2}=6x is

Correct option: (c)

Smaller area enclosed by the circle x^{2}+y^{2}=4 and the line x + y =2 is

- 2(π-2)
- π-2
- 2π-1
- 2(π+2)

Correct option: (b)

Area lying between the curves y^{2}=4x and y = 2x is

Correct option: (b)

Area lying in first quadrant and bounded by the circle x^{2}+y^{2}=4 and the lines x =0 and x =2, is

Correct option: (a)

Area of the region bounded by the curve y^{2}=4x ,y-axis and the line y =3, is

Correct option: (b)

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