- #1

- 57

- 1

## Homework Statement

Give the complex fourier series for [tex]f(x) = 2 - x, -2<x<2[/tex]

## Homework Equations

[tex]f(x) = \sum_{n=-\infty}^\infty C_ne^{\frac{i n \pi x}{l}[/tex]

[tex]C_n=\frac{1}{2l} \int_{-l}^l f(x)e^{\frac{-i n \pi x}{2}} dx [/tex]

## The Attempt at a Solution

[tex]f(x) = 2 - x, l = 2[/tex]

[tex]f(x) = \sum_{n=-\infty}^\infty \frac{1}{4} \int_{-2}^2 ((2-x)e^{\frac{-i n \pi x}{2}}dx) e^{\frac{i n \pi x}{2} [/tex]

now here, I don't know which steps I should take next. Should I take this integral for general n? Or should I break it up into the case for when n=0, n>0, and n<0?

I've kind of tried both to no avail :(