Evaluate

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- November 30th 2007, 05:48 PMliyiSine integral
Evaluate

- November 30th 2007, 06:06 PMkalagota
- November 30th 2007, 06:22 PMgalactus
I don't think sin(x)/x is readily done by parts or any other elementary operation. This is a case for PH's forte, complex analysis.

You can start by using , because it has a simple pole at z=0 and has a residue

I have been studying a little CA when I have time, but don't have my sea legs yet. - November 30th 2007, 06:40 PMkalagota
yeah, i was solving it using ibp but i don't get anything useful..

about using CA concepts, it is possible if s/he has taken the course.. personally, i haven't taken it so i can't even use it.. Ü - November 30th 2007, 07:00 PMKrizalid
- December 1st 2007, 03:34 AMgalactus
Whoa, Kriz, you show off you. I am now bowing to the master. Very clever indeed.(Clapping)

- December 1st 2007, 02:20 PMThePerfectHacker
Let . Consider the square contour (for large) from to with be a semicircular contour from to (for small).

Then by Cauchy's theorem*:

Now make to get:

Equate real and imaginary parts.

*)The issue of convergence is covered by Jordan's lemma.