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Need help with a integral.

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    Orthogonality relations:

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

    over the interval -pi to pi.
    3. The attempt at a solution

    Using the orthogonality relation I figured the answer would be 1/a*a for m=1, and 0 for [tex]n \neq m[/tex]. However for a particular problem the book says there is a solution for [tex]n \neq m[/tex]. Is there a better way to go about this particular integral?
     
  2. jcsd
  3. Apr 9, 2009 #2
    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.
     
  4. Apr 9, 2009 #3
    Ah alright thanks very much.
     
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