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Find the Fourier cosine series of f(x)=x(Pi+x)

  1. Aug 22, 2011 #1
    The problem statement, all variables and given/known data
    Find the Fourier cosine series representation of
    g([itex]\chi[/itex]) = [itex]\chi[/itex] ([itex]\pi[/itex] + [itex]\chi[/itex])
    on the interval (0,[itex]\pi[/itex])


    The attempt at a solution
    Okay so I've got
    a0=[itex]\frac{1}{\pi}[/itex][itex]\int\chi(\pi+\chi)d\chi[/itex]

    =[itex]\frac{5\pi^{3}}{6}[/itex]

    an=[itex]\frac{1}{\pi}[/itex][itex]\int\chi(\pi+\chi)cos(n\chi)d\chi[/itex] for n[itex]\geq1[/itex]

    But I'm not quite sure where to go from there
     
  2. jcsd
  3. Aug 22, 2011 #2
    Distribute the χ so you have the integral of the sum of two terms. This can be separated into two integrals (linear property of integration).

    Both of these integrals can be solved using integration by parts.
     
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