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

int_(0)^((pi)/(2))log(sin2x)dx

int_(0)^( pi)cos2x*log(sin x)dx

Evaluate: int_(0)^( pi)x log sin xdx

Evaluate int_(0)^( pi)x log sin xdx

int_(0)^( pi/2)ln(sin^(2)x cos 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 .