Question

The value of `int _(0)^(pi//2) (2^(sinx))/(2^(sinx)+2^(cosx))dx` is
A. 2
B. `pi`
C. `pi/4`
D. `2pi`

Answer 1

Correct Answer - C
Let `l=int_(0)^(pi//2)(2^(sinx))/(2^(sinx)+2^(cosx))dx" ...(i)"`
`rArr" "l=int_(0)^(pi//2)(2^(cosx))/(2^(cosx)+2^(sinx))dx" ...(ii)"`
On adding Eqs. (i) and (ii), we get
`2l=int_(0)^(pi//2)1dx=(pi)/(2)`
`rArr" l=(pi)/(4)`