# Thread: How to calculate this

1. ## How to calculate this

Okay, so I have this reduction formulae question
Establish a reduction formula to find Im,n =∫cos m x . sin n x dx
Prove that (m+n). Im,n = (m-1) . Im-2,n

And okay I solve the problem above, but then the question says
evaluate I5,6

and I can't find the value 8/693 which is the answer in answer key. I'm so confused, what I need to do is just substituting the value right?
But the problem is the I is the integral of ∫cos m x . sin n x dx so what to do with x, do we just put whatever on x, or what?

2. ## Re: How to calculate this

You forgot to mention the limits of integration, which I think are 0 to $\displaystyle \pi/2$.

You use the reduction formula twice to get $\displaystyle I_{5,6}$ = some number times $\displaystyle I_{1,6}$. Then $\displaystyle I_{1,6}=\int_0^{\pi/2}\cos{x}\sin^6{x}\,dx$ can be integrated by substituting $\displaystyle u=\sin{x}$.

- Hollywood

3. ## Re: How to calculate this

Thanks for your help . I understand this now