This is a group challenge:

It's well known that $\displaystyle \displaystyle \int_0^\infty \frac{\sin x}{x}dx = \frac{\pi}{2} $.

I know of a few ways of showing this. My challenge to all of you is to come up with as many ways as you can to prove this result.

Let's see if there's any ways I'm not aware of yet! (Wink)