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.

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- May 1st 2009, 09:29 AMLanceyPantsMore Calculus Final
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. - May 1st 2009, 09:46 AMadhyeta
rewrite the thing as:

http://latex.codecogs.com/gif.latex?...\pi}{n}x%20)dx

try it out now.

(Happy) - May 1st 2009, 09:47 AMe^(i*pi)
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__: