Originally Posted by

**shmounal** Hi, I'm doing some questions on the mean value theorem and while I understand the theory in my set of answers they tend to jump from integrating compex trig functions to just giving the answer so if someone could explain how to go from

$\displaystyle 1$/$\displaystyle 2\pi$$\displaystyle \int_{0}^{2\pi}$$\displaystyle \cos^2$$\displaystyle \theta$$\displaystyle \sin$ $\displaystyle \theta$$\displaystyle d$$\displaystyle \theta $

to the answer given as

-(cos^3 $\displaystyle \theta $\6) between $\displaystyle 0$ and $\displaystyle 2\pi$ which obviously equals 0. If someone could give me a step by step explanation of how to get from the initial integral to the answer I'd be very greatful. I've tried plugging in quite a few different trig identities but I just get into a mess!!

Cheers!

P.S. sorry I gave up with latex.. too frustrating to get it to give the right output but hopefully post still makes sense!