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The value of int (0)^(pi//2)(sin ^(2)x-...

The value of `int _(0)^(pi//2)(sin ^(2)x-cos ^(2)x)/(sin ^(3)x+cos^(3)x)dx ` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l =int _(0)^(pi//2)((sin ^(2)x-cos ^(2)x)dx)/((sinx+cos x))`
`(sin^(2)x+cos ^(2)x-sinx cos x)`
`l=int_(0)^(pi//2)((sin x-cosx)dx)/((1-sinx cos x))`
`[becauseint_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx]`
`impliesl=0`
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