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Given int(0)^(pi//2)(dx)/(1+sinx+cosx)=A...

Given `int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A`. Then the value of the definite integral `int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx` is equal to

A

`1/2A`

B

`(pi)/2-A`

C

`(pi)/4-1/2A`

D

`(pi)/2+A`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_(0)^(pi//2) (sinxdx)/(1+sinx+cosx)=int_(0)^(pi//2)(cos xdx)/(1+sinx+cosx)`
or `2I=int_(0)^(pi//2)(sinx+cosx+1-1)/(sinx+cosx+1)dx`
`2I=(pi)/2A`
or `I=(pi)/4-1/2A`
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