# Short Fourier series question

## Homework Equations

Usual equations for calculating fourier series coefficients

## The Attempt at a Solution

Well essentially I don't know what to let f(x) equal to for calculating the coefficients a0, an and bn. Should I use 1 + x/pi or 1 - x/pi? And what about the limits? I was thinking maybe between -pi and pi.

Anyway here's my progress thus far, I think the graph is ok anyways.

Thanks dudes. I would use latex but I suck at it :yuck:

I like Serena
Homework Helper
Looks fine.
The integral can be calculated by splitting it into the sum of 2 integrals.

Take for example:

$$a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx$$

now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

$$a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)$$

However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.

Take for example:

$$a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx$$

now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

$$a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)$$

However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.

Looks fine.