int_(0)^( pi)x ln(sin x)dx=

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

If int_(0)^(pi)x f(sin x) dx = a int_(0)^(pi)f (sin x) dx , then a =

underset is If int_(0)^( pi)xf(sin x)dx=A int_(0)^((pi)/(2))f(sin x)dx, then A

If I_(1) = int_(0)^(pi//2)ln (sin x)dx , I_(2)=int_(-pi//4)^(pi//4)ln (sin x + cos x)dx , then :

Using integral int_(0)^(-(pi)/(2))ln(sin x)dx=-int_(0)^( pi)ln(sec x)dx=-(pi)/(2)ln2 and int_(0)^((pi)/(2))ln(tan x)dx=0 and int_(0)^((pi)/(4))ln(1+tan x)dx=(pi)/(8)

The value of the integral int_(0)^(pi)x log sin x dx is

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=