I've been working my way through Intro to Electrodynamics (Griffiths), and in Chapter 3, one of the derivations comes out to(adsbygoogle = window.adsbygoogle || []).push({});

∫sin(n[itex]\pi[/itex]y/a) sin(n'[itex]\pi[/itex]y/a) dy ={ 0 if n'[itex]\neq[/itex]n

a/2 if n'=n

where the function is integrated from 0 to a.

I assume there is some logical interpretation that allows me to reduce the answer down to just those two cases, but for the life of me I cannot figure out how. He skips over it as if it were trivial. Maybe it is supposed to be, but I didn't have any issues with all of the PDE's, so I find it frustrating that this is causing such a gap in my understanding.

If it is of any help, that answer I got is :

(an*sin([itex]\pi[/itex]m)cos([itex]\pi[/itex]n)-am*cos([itex]\pi[/itex]m)sin([itex]\pi[/itex]n)

/([itex]\pi[/itex](m^2-n^2))

edit: if anyone has the book, it is possible that I'm just no seeing a previous relation that simplifies this, so it may help to look

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

Dismiss Notice

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!

# Don't understand critical part of derivation in textbook.

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