# Thread: variable sustitution

1. ## variable sustitution

Someone knows how to demostrate

Integral (senxcosx)^m, {0,Pi/2}=2^m·Integral(cosx)^m, {0,Pi/2}???

Thanks by hand

2. ## Re: variable sustitution

Hey nigromante.

Is your senx sin(x), or sec(x), (or something else)?

3. ## Re: variable sustitution

It's sin(x). The Spanish (and Italian) word for sine is seno, so they use sen(x) instead of sin(x).

Here's a start:

$\int_0^{\frac{\pi}{2}}(\sin{x}\cos{x})^m\ dx=2^{-m}\int_0^{\frac{\pi}{2}}(\sin{2x})^m\ dx$

which uses the identity $\sin{2u}=2\sin{u}\cos{u}$. It looks like you might want to use the identity $\sin{u}=\cos{\left(\frac{\pi}{2}-u\right)}$. I'm pretty sure you'll need to have $2^{-m}$ instead of $2^m$.

- Hollywood

4. ## Re: variable sustitution

Thanks for your answers, Holliwood is right, I'm mexican, and is again right, I need 2^-m. Thanks again to all.