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

Prove the following : 0 lt int_(0)^(pi//2)sin^(n+1)xdx lt int_(0)^(pi//2)sin^(2)xdx, n gt 1

Prove the following : 0 lt int_(0)^(pi//2)sin^(n+1)xdx lt int_(0)^(pi//2)sin^(2)xdx, n gt 1

If a, b,c are the values of int_(0)^(pi//2)sin^(6)xdx,int_(0)^(pi)sin^(6)xdx,int_(0)^(2pi)sin^(6)xdx then the ascending order of a, b, c is

int_(0)^(pi//2)sin^(2)xdx=?

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

int_(0)^(pi//2)sin^(9)xdx=

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

int_(0)^( pi/4)sin^(4)xdx

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

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