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

int_(0)^((pi)/(4))log sin2xdx equals to

int_(0)^((pi)/(2))log cos xdx equals

int_(0)^((pi)/(2)) sin^7 xdx is :

int_(0)^((pi)/(2))sin^5 xdx= .

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

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

Show that, int_(0)^(pi)sin^(4)xdx=2int_(0)^((pi)/(2))sin^(4)xdx , hence, find the value of int_(0)^(pi)sin^(4)xdx .

Show that, int_(0)^(pi)sin^(3)xdx=2int_(0)^((pi)/(2))sin^(3)xdx and hence, find the value of int_(0)^(pi)sin^(3)xdx .

Show that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=pi/4 .

Prove that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=(pi)/(4)