- #1
saybrook1
- 101
- 4
Homework Statement
I need to find the Fourier series for [itex]f(x)=|x|^3[/itex].
Homework Equations
[itex]f(x)=|x|^3[/itex]
[itex]A_n=\frac{2}{L}\int_{0}^{L}|x|^3cos{\frac{n\pi x}{L}}dx[/itex]
[itex]\int_{0}^{L}x|x|sin{\frac{n\pi x}{L}}dx[/itex]
The Attempt at a Solution
Since it is an even function I know that it will be a cosine series and so I set out to find the A coefficient like so:
[itex]A_n=\frac{2}{L}\int_{0}^{L}|x|^3cos{\frac{n\pi x}{L}}dx[/itex]
Through integration by parts I end up with a sine term that goes to zero and some coefficients out in front of an integral that looks like:
[itex]\int_{0}^{L}x|x|sin{\frac{n\pi x}{L}}dx[/itex]
I would really appreciate any help with this particular integral or if someone could point me in the direction of a solution where a Fourier series is calculated for a function with an absolute value to the power>2. Thanks in advance.