Need some help with an integral

Asked Oct 16 '18 at 04:54

Active Oct 16 '18 at 04:59

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I was reading on integration techniques and a came across an example that is shown quite a lot around the web.

$$ \int_0^\infty \frac {\sin(x)}{x}\,dx $$

I do know the answer must be $\frac {\pi}{2}$.

There are many ways to solve this but I am interested in differentiation under the integral sign. I am sorry but I am having trouble grasping the concept.

Could someone please go over this integral with me in a more elementary way (kind of step-by step)?

Thank you so much for your help and time!

edited Oct 16 '18 at 04:59

Masacroso

30,417

asked Oct 16 '18 at 04:54

Apple

More specifically, this answer by xpaul explains how to solve the particular integral using differentiation under the integral sign – Ben Grossmann Oct 16 '18 at 05:01
thank you all for the comments , i will check these out! – Apple Oct 16 '18 at 05:03
@Omnomnomnom unfortunately the answer you linked is not the best. Indeed it is not clear that it is correct as stated. – Masacroso Oct 16 '18 at 05:11
Indeed you'll find many proofs in the link posted by Kemono Chen. More precisely, this answer in the link uses differentiation under the integral sign. – Scientifica Oct 16 '18 at 09:27

Need some help with an integral

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