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

  • Thread starter Nallyfish
  • Start date
  • #1
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Homework Statement
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
 

Answers and Replies

  • #2
764
71
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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