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IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx ,...

`IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx ,` Then show that `I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N)` Hence, prove that `I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4` when both `m` and `n` are even
`((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}`

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