39.int_(0)^((pi)/(2))cos xdx=?

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

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

int_(0)^((pi)/(2))cos^(4)xdx

int_(0)^((pi)/(2))cos^(8)xdx

If I_(I)=int_(0)^( pi/2)cos(sin x)dx,I_(2)=int_(0)^((pi)/(2))sin(cos x)d, and I_(3)=int_(0)^((pi)/(2))cos xdx then find the order in which the values I_(1),I_(2),I_(3), exist.

int_(0)^((pi)/(4))cos^(2)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)

Evaluate the definite integrals int_(0)^((pi)/(2))cos2xdx

int_(0)^((pi)/(2))cos^(5)xdx=(8)/(15)