# Fourier Series of Triangular waveform

Fourier Series of Triangular waveform

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

and from 0 to +π the equation of the waveform is

Which gives

My question is,

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

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

But this gives

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

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