Question

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`

Answer 1

Correct Answer - 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`