I'm given a problem and the answer. I get credit for working the steps from beginning to end.
$\displaystyle \int \sin^2 ((\pi/n) x) dx$
Any help would be amazing.
Let $\displaystyle \alpha = \frac{\pi}{n}$:
$\displaystyle \int \sin^2(\alpha x)$
Remember that $\displaystyle cos(2\alpha x) = 1-2sin^(\alpha x)$ therefore $\displaystyle sin^2(\alpha x) = \frac{1-cos(2\alpha x)}{2} = \frac{1}{2} - \frac{cos(2\alpha x)}{2}$
$\displaystyle I = \frac{1}{2} - \int \frac{cos(2\alpha x)}{2}$
where I is the integral.
Spoiler: