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## Homework Statement

[/B]

[tex]

f(x)=\left\{\begin{array}{cc}0,&\mbox{ if }

0< x < 2\\1, & \mbox{ if } 2<x<4\end{array}\right.

[/tex]

Show that the Cosine Fourier Series of f(x) for the range [0,4] is given by:

[tex] A + B\sum^{\infty}_{n=0}\frac{(-1)^n}{(2m+1)}cos(\frac{(2m +1) \pi x}{2})[/tex]

## Homework Equations

[tex]a_n = \frac{2}{L}\int^{x_0 + L}_{x_0} f(x)cos(\frac{2\pi nx}{L})dx[/tex]

## The Attempt at a Solution

L = 4

[tex]a_n = \frac{1}{2}\int^{4}_{0} f(x)cos(\frac{\pi nx}{2})dx =\frac{1}{2}\int^{2}_{0} 0cos(\frac{\pi nx}{2})dx+\frac{1}{2}\int^{4}_{2} cos(\frac{\pi nx}{2})dx = \frac{1}{2}\int^{4}_{2} cos(\frac{\pi nx}{2})dx[/tex]

[tex] = \frac{1}{2}[\frac{2 sin(2n\pi)}{\pi n} - \frac{2 sin(n\pi)}{\pi n} = \frac{1}{2}[0 - 0] = 0[/tex]

I do get a non-zero a

_{0}term but it seems weird to me that B would be zero, is my L wrong?

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