More Calculus Final

**LanceyPants** · May 1st 2009, 09:29 AM

I'm given a problem and the answer. I get credit for working the steps from beginning to end.

$\int \sin^2 ((\pi/n) x) dx$

Any help would be amazing.

**adhyeta** · May 1st 2009, 09:46 AM

Originally Posted by LanceyPants

I'm given a problem and the answer. I get credit for working the steps from beginning to end.

$\int \sin^2 ((\pi/n) x) dx$

Any help would be amazing.

rewrite the thing as:

$\frac{1}{2}\int (1-cos\frac{2\pi}{n}x )dx$

try it out now.

**e^(i*pi)** · May 1st 2009, 09:47 AM

Originally Posted by LanceyPants

I'm given a problem and the answer. I get credit for working the steps from beginning to end.

$\int \sin^2 ((\pi/n) x) dx$

Any help would be amazing.

Let $\alpha = \frac{\pi}{n}$ :

$\int \sin^2(\alpha x)$

Remember that $cos(2\alpha x) = 1-2sin^(\alpha x)$ therefore $sin^2(\alpha x) = \frac{1-cos(2\alpha x)}{2} = \frac{1}{2} - \frac{cos(2\alpha x)}{2}$

$I = \frac{1}{2} - \int \frac{cos(2\alpha x)}{2}$

where I is the integral.

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