Integral of trigonometric functions

[darkmagic]

Homework Statement

How can I integrate this:

$$\int sin (nt) sin (n \pi t) dt$$

This actually in the Fourier series.

 

[LCKurtz]

Use the trig identity:

$$\sin\theta\sin\phi=\frac{\cos{(\theta-\phi)}-\cos{(\theta+\phi)}}{2}$$

 

[Donaldos]

You can use the following identity:

$$\sin a \sin b=\frac{\cos(a-b)-\cos(a+b)} 2$$