# Fourier series and the dirchlet integral

1. Jun 5, 2008

### dirk_mec1

Use a Fourier series to prove that: $$\int_{0}^{ \infty} \frac{\sin(x)}{x}\ \mbox{d}x = \frac{ \pi}{2}$$

What function do I need to fourier transform?

2. Jun 7, 2008

### Pere Callahan

There aren't many to choose from are they? I suggest you try Fourier-transforming sin(x) and sin(x)/x and see where it leads you.

3. Jun 7, 2008

### dirk_mec1

Actually there are and I found that there are two ways of finding this answer both NOT with solely a sin(x) or sin(x)/x. I'm suprised that you didn't took the effort to look more closely to the question at hand.

4. Jun 7, 2008

### Pere Callahan

You're right. In particular I read Fouriertransform instead of Fourier Series. You're also right in saying that transforming sin(x) or sin(x)/x seems not to provide an easy solution to the problem.

Which two ways are you referring to? One is likely to Laplace-transform 1/x ..?