`int_(0)^(pi) sinx cos^(2)xdx`

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

Consider the definite integrals A=int_(0)^(pi)sinx cosx^(2)xdx and B=int_(0)^((pi)/(2))sinx cos^(2)xdx . Then,

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

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

int_(0)^(pi) sin^(4) x cos^(2)xdx =

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

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

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

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

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