PROBLEM 2
Show that the function $f(x) = ax^2$ over the range $x = 0$ to $x = L$, $a$ is a constant, can be
represented by a Fourier series, $f(x) = \sum_{n} A_n \sin(\frac{n\pi}{L}x)$ where
$A_n = \frac{2aL^2}{n^3\pi^3}[(2 - n^2\pi^2)cos n\pi - 2]$.
Use online Desmos graphing tool (as shown in the class) to show that this series indeed
approximates the function $f(x) = ax^2$.
