`int_(0)^( pi/2)log sin xdx`

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

int_(0)^(pi) x log sinx dx

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

The value of int_(0)^(pi//2) (2log sin x-log sin 2x)dx , is

int_(0)^(pi) x log sinx\ dx

Evaluate int_(0)^(pi//2)lnsin2xdx

Evaluate: int_(0)^((pi)/(2)) log (sin x) dx

(i) int_(0)^( pi/2)x cos xdx

Evaluate : int_(0)^(pi/2)log(tanx)dx