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 ?


marked as duplicate by user17762, J. M. is a poor mathematician, David Mitra, AD., davidlowryduda 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.


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



Not the answer you're looking for? Browse other questions tagged or ask your own question.