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How do I go about calculating the fourier series of:

$$x(π-|x|)$$ $$over $$$$[-π,π]$$

I notice that it is an odd function, therefore a0 and an equal 0, therefore we only have to find bn. However I don't understand how to deal with the modulus function as above when solving for this specific fourier series. Any attempts in solving this will be greatly appreciated!

Arv
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    As usual, eliminate $|...|$ by decomposing the integral into two ones : $b_n=k(\int_{-\pi}^0 x(\pi+x)\sin(2 \pi n x)dx... +\int_0^{\pi}x(\pi-x)\sin(2 \pi n x)dx...)$ – Jean Marie May 12 '19 at 13:22
  • The answer is $$\sum_{k=0}^\infty \frac{8\sin{((2k+1)x)}}{\pi(2k+1)^3}$$ – Peter Foreman May 12 '19 at 13:28

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