Definite Integration 

Asked by priyagpihu111 | 20th Jul, 2020, 01:54: PM

Expert Answer:

TO find the integral of {2x}/{2x+22014-x} between the limits 0 and 2014
 
I equals integral subscript 0 superscript 2014 fraction numerator 2 to the power of x over denominator 2 to the power of x plus 2 to the power of 2014 minus x end exponent end fraction d x
equals integral subscript 0 superscript 2014 fraction numerator 1 over denominator 1 plus 2 to the power of 2014 minus 2 x end exponent end fraction d x
equals integral subscript 0 superscript 2014 fraction numerator 1 over denominator 1 plus 2 to the power of 2 left parenthesis 1007 minus x right parenthesis end exponent end fraction d x
T a k e space 1007 minus x equals t
D i f f e r e n t i a t i n g space w. r. t space x comma space w e space g e t
d x equals negative d t
W h e n space x equals 0 space rightwards double arrow t equals 1007
W h e n space x equals 2014 space rightwards double arrow space t equals negative 1007
I equals integral subscript negative 1007 end subscript superscript 1007 fraction numerator d t over denominator 1 plus 4 to the power of t end fraction

Answered by Renu Varma | 25th Jul, 2020, 05:48: PM

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