Simple Integration

**jegues** · October 25th 2012, 04:10 PM

Can someone clarify this integral for me?

EDIT: I figured it out, brain fart!

$\int_{\alpha}^{\pi-\alpha}sin(n\omega_{o}t)d(\omega_{o}t) =-\frac{1}{n} \left( cos(n(\pi-\alpha)) - cos(n\alpha) \right) = \frac{1}{n} \left( -cos(n\alpha)) - cos(n\alpha) \right) = \frac{2}{n}cos(n\alpha)$

**johnsomeone** · October 25th 2012, 07:16 PM

$\int_{t = \alpha}^{t = \pi-\alpha} \sin(n\omega_{o}t)d(\omega_{o}t) = \left \frac{-\cos(n\omega_{o}t)}{n} \ \right]_{t = \alpha}^{t = \pi-\alpha} =-\frac{1}{n} \left( \cos(n\omega_{o}(\pi-\alpha)) - \cos(n\omega_{o}\alpha) \right)$

$= \frac{1}{n} \left( -\cos(n\omega_{o}\pi - n\omega_{o}\alpha) + \cos(n\omega_{o}\alpha) \right)$

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