Reduction Formula: If `I_n = int_0 ^(pi/2) sin^nx = (n-1)/n I_(n-2)` and find `I_n` in terms of n for n being odd or even.

Find the reduction formula for int_(0)^((pi)/(2))sin^(n)xdx

If I_(n)=int_(0)^((pi)/(2))(sin^(2)nx)/(sin^(2)x)dx, then

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

If I_(m;n)=int_(0)^((pi)/(2))sin^(m)x cos^(n)xdx then show that I_(m;n)=(m-1)/(m+n)I_(m-2;n) and find I_(m;n) in terms of different combinations of m and n.