Originally Posted by

**FalconPUNCH!** Well I think I got the answer and it took me about two pages to get it trail and error.

Here's how I approached it:

I substituted $\displaystyle Sin^{2}t$ with $\displaystyle 1 - cos^{2}t$

$\displaystyle \int_{0}^{Pi} (1-cos^{2}t) (cos^{2}t) (cos^{2}t)$

I used half angle formula to get

$\displaystyle \frac{1}{8} \int_{0}^{Pi} (1- \frac{1}{2}[1+cos^{2}t])(\frac{1}{2}[1+cos^{2}t])(\frac{1}{2}[1+cos^{2}t])$

I expanded everything and got

$\displaystyle \frac{1}{8}\int_{0}^{Pi} 2cos2t + cos^{2}t * cost dt $

I went from there and did a few more steps and got $\displaystyle \frac{29Pi}{128}$

Can anyone check if I did it correct?