Struggling with Fourier Series Coefficient Integral for PDE Solution?

[inko1nsiderat]

Homework Statement

The problem is in the solution to a PDE, the coefficient for the Fourier series is of some form like a_n=\frac{1}{a}\int cos(nx)cos(x) dx over the interval -a to a.

Homework Equations

Orthogonality relations:

\int cos(nx) cos(mx) dx =[ 0, n \neq m, pi n=m \neq 0

over the interval -pi to pi.

The Attempt at a Solution

Using the orthogonality relation I figured the answer would be 1/a*a for m=1, and 0 for n \neq m. However for a particular problem the book says there is a solution for n \neq m. Is there a better way to go about this particular integral?

 

[Billy Bob]

If a is not pi, then you can't use the orthogonality relation. This assumes your integral in step 1 is set up correctly. To evaluate it, just find the antiderivative and use FTC. Any decent table of integrals will have the antiderivative. There are two cases, n=1 and otherwise.

 

[inko1nsiderat]

If a is not pi, then you can't use the orthogonality relation. This assumes your integral in step 1 is set up correctly. To evaluate it, just find the antiderivative and use FTC. Any decent table of integrals will have the antiderivative. There are two cases, n=1 and otherwise.

Ah alright thanks very much.