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Possible Duplicate:
Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?

How to prove $$\int^{\infty}_{0}\frac{\sin x}{x}\mathrm{d}x=\frac{\pi}{2}$$ Do you have a simple method ?

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marked as duplicate by Marvis, J. M., David Mitra, AD., mixedmath Apr 29 '12 at 5:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Duplicate: – user23784 Apr 29 '12 at 4:48

This is known as the Dirichlet integral. A couple of different derivations appear on the Wikipedia page:

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