Someone knows how to demostrate
Integral (senxcosx)^m, {0,Pi/2}=2^m·Integral(cosx)^m, {0,Pi/2}???
Thanks by hand
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:
$\displaystyle \int_0^{\frac{\pi}{2}}(\sin{x}\cos{x})^m\ dx=2^{-m}\int_0^{\frac{\pi}{2}}(\sin{2x})^m\ dx$
which uses the identity $\displaystyle \sin{2u}=2\sin{u}\cos{u}$. It looks like you might want to use the identity $\displaystyle \sin{u}=\cos{\left(\frac{\pi}{2}-u\right)}$. I'm pretty sure you'll need to have $\displaystyle 2^{-m}$ instead of $\displaystyle 2^m$.
- Hollywood