hiiiii

 

Well there is a famous result which is as follows ...

 

₀^/2 sin^mx.cosⁿx.dx  = (G(m+1/2)G(n+1/2))/2.G((m+n+2)/2)

 

where G is gamma function and it satisfies the following properties ..

 

(i) G(1) = 1  and G(n+1) = n.G(n)

 

(ii) G(n+1) = n! if n is a natural number

 

(iii) G(1/2) =  

 

 

Let me give you some advice ... whenever u see limit between 0 to /2 and sinx , cosx terms ... do try to use this formula .. it is very useful and shud be learnt by heart ..

 

cheers