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

Evaluate the following definite integral: int_(0)^( pi/2)x^(2)cos2xdx

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)

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

Evaluate: I=int_(0)^(2 pi)x*cos^(5)xdx

Evaluate : int_(0)^(pi) cos^(2)x.dx

Prove that, int_(-(pi)/(2))^((pi)/(2))cos^(3)xdx=2int_(0)^((pi)/(2))cos^(3)xdx , hence, find the value of int_(-(pi)/(2))^((pi)/(2))cos^(3)xdx

Show that, int_(-(pi)/(2))^((pi)/(2))cos^(5)xdx=2int_(0)^((pi)/(2))cos^(5)xdx and find the value of int_(-(pi)/(2))^((pi)/(2))cos^(5)xdx .

int_(0)^( pi/2)sin^(8)x cos^(2)xdx=

int_(0)^( pi/2)sin^(3)x*cos^(2)xdx