" (i) "int_(0)^( pi)x cos^(2)xdx

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

int_(0)^(2 pi)cos^(7)xdx

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

int_(0)^(2 pi)cos^(5)xdx=

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

int_(0)^( pi/2)cos^(6)xdx

int_(0)^( pi/2)cos^(3)xdx

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

prove that int_(0)^( pi)x cos^(2)xdx=(pi^(2))/(4)

STATEMENT 1:int_(0)^( pi)x sin x cos^(2)xdx=(pi)/(2)int_(0)^( pi)sin x cos^(2)xdxint_(b)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx