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Fourier Series of Triangular waveform

http://i64.tinypic.com/w0mku9.jpg

this is the solution of Fourier series of a triangular waveform from the book Circuits and Networks: Analysis and Synthesis by Shyammohan S. Palli. In this problem they have take the time period of the triangular waveform from -π to +π instead of 0 to 2π.

Now, from -π to 0 the equation of the waveform is as shown below

enter image description here and from 0 to +π the equation of the waveform is

enter image description here Which gives

enter image description here My question is,

If i take the interval from 0 to 2π.then from 0 to +π the equation of the waveform will be

enter image description here

and from +π to +2π the equation of the waveform will be

enter image description here

But this gives

enter image description here

which did not match with previous.My question is why they took the interval from -π to +π instead of 0 to 2π.

I will post my calculation here

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  • $\begingroup$ Without seeing your actual solution, the result should be the same. Taking the interval as $[0, 2\pi]$, the average value is: $$a_0 = \frac{1}{2\pi}\int_0^{2\pi}\nu(t)\mathrm{d}t=\frac{1}{2\pi}\int_0^{\pi}\ \left(10 - \frac{10}{\pi}t\right)\mathrm{d}t + \frac{1}{2\pi}\int_{\pi}^{2\pi}\ \left(\frac{10}{\pi}t - 10\right)\mathrm{d}t=5$$ $\endgroup$ – Winter Soldier Feb 13 at 16:20

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