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

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

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