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

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

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

int_(0)^(pi//2)(sin^(2)xdx)/((1+cosx)^(2))= ………

The value int_(0)^(pi//2) sin^(2)xdx will be :

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