`int_(0)^(pi//2) log sin x dx =`

If I_(1)= int_(0)^(pi//2) x sin x dx and I_(2)=int_(0)^(pi//2) x cos x dx, then which one of the following is true ?

int_0^(pi//2) log(tan x)dx =

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .

int_(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

If int_0^pi x f (sin x)dx = A int_0^(pi//2) f (sin x) dx , then A is :

If int_0^(pi) x f (sin x) dx = A int_0^(pi//2) f (sin x) dx , then A is :

int_0^(pi//2) log(tan x) dx is :

int_0^(pi//2) cos x e^(sin x) dx is :

int_(0)^(pi) log(1 + cos x)dx .