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## Homework Statement

A function [itex] F(x) = x(L-x) [/itex] between zero and L. Use the basis of the preceding problem to write this vector in terms of its components:

[itex]F(x)= \sum_{n=1}^{\infty}\alpha _{n}\vec{e_{n}}[/itex]

If you take the result of using this basis and write the resulting function outside the interval [itex]0<x<L[/itex], graph the result

## Homework Equations

The basis as mentioned above is [itex]\vec{e_{n}}=\sqrt{\frac{2}{L}}\sin {\frac{n\pi x}{L}}[/itex]

## The Attempt at a Solution

I don't really know where to start, do I just need to write F(x) as a fourier series and then compute the coefficients using the standard "trick" to do so, ie sticking F(x) in the integral and so on?

The previous problem was just showing that the basis is orthonormal.