(adsbygoogle = window.adsbygoogle || []).push({}); Orthogonal Properties for Sine Don't Hold if Pi is involded??

Normally I know [tex]

\int_{-L}^L \sin \frac{n x}{L} \sin \frac{\m x}{L} ~ dx = 0\mbox{ if }n\not =m , \ =L \mbox{ if }n=m

[/tex] but apparently this doesn't work for [tex]

\int_{-L}^L \sin \frac{\pi n x}{L} \sin \frac{\pi m x}{L} ~ dx

[/tex]

I am trying to find fourier coefficients, and my integral is [tex]\int_{0}^{L/2} \sin \frac{2\pi x}{L} \sin \frac{\pi n x}{L} ~ dx

[/tex]

For even n that aren't 2, the integral is 0, if n=2, then the integral is L/2, but if n is odd, then the integral doesn't equal 0 (it's actually a fairly complex answer) even thought it looks like it should by orthogonal properties ...why doesn't this work?

The integrals I am doing take very long to do, is there a property that would allow me to shorten them?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orthogonal Properties for Sine Don't Hold if Pi is involded?

**Physics Forums | Science Articles, Homework Help, Discussion**