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Fourier series (integration of pi)

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi

    First of all this a text book question from Stroud Advanced Engineering Mathematics, solution is given, but no steps are shown.

    A question I just cant seem to solve at the moment, as below.

    A function f(x) is defined by [tex]f(x) = \pi - x:0 < x < \pi[/tex]
    [tex] f(x + 2\pi) = f(x)[/tex]

    Express the function as a half range cosie series

    2. Relevant equations

    Im at a loss of how to start this question, Ive been doing fine when they havent included pi in the function itself.

    I know as its wanted as a cosine series I'll have to make it resemble an even function and thus my a0 and an terms can be

    [tex]2/\pi \int^{\pi}_{0}\pi - x dx[/tex]


    [tex]\stackrel{2}{\pi}\int^{\pi}_{0}\pi - x\:cosnx:dx[/tex]

    So my main question is really how I remove pi. Ive tried taking it out as a constant which doesnt work, so I have a feeling Im not realising something

    The final solution according to the book is

    [tex] \pi/2 + 4/\pi\left\{cosx + 1/9:cos3x + 1/25:cos5x+ ...\right\}[/tex]

    I keep getting [tex] -\pi^2[/tex] for a0

    Thank you for reading and any help
     
    Last edited: Apr 12, 2010
  2. jcsd
  3. Apr 12, 2010 #2

    LCKurtz

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    Since you haven't actually shown what you did, I will make a wild guess that your problem is caused by leaving the parentheses out:

    [tex]\stackrel{2}{\pi}\int^{\pi}_{0}(\pi - x)\:cosnx\ dx[/tex]

    You don't treat [itex]\pi[/itex] any differently than you would treat a number like 5.
     
  4. Apr 14, 2010 #3
    Hi

    Thanks for the reply, sorry I didnt put down more of my working, I was having trouble using the Latex. I have solved the problem as I was forgetting the a0/2 term, and didnt correctly integrate the -pi term.
     
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