# Thread: Interval problem in Fourier series

1. ## Interval problem in Fourier series

The functions are-
$\displaystyle (a) f(x)=\left | x \right |, -\pi\leq x\leq \pi$
$\displaystyle (b) f(x)=\left | sin x \right |, -\pi\leq x\leq \pi$
Writing them individually
a)$\displaystyle f(x)=x$ and $\displaystyle f(x)=-x$
b)$\displaystyle f(x)=sin x$ and $\displaystyle f(x)=-sin x$
The problem is what should be the correct intervals for these functions. I am pretty messed up with this basic thing though I can easily compute the fourier series of these functions.

2. Basically you need to identify two things:
1) What values of x make the expression inside the absolute value sign positive?
2) What values of x make it negative?

The first problem is simple, but we have to take into account that the domain is $\displaystyle -\pi<x<\pi$.

$\displaystyle f(x)=|x|=\begin{cases} x, & 0 \le x \le \pi \\ -x, & -\pi \le x < 0 \end{cases}$

Does this make sense? Can you figure out the second one like this?