I need to show that:

It seems obvious that i need to use

but I can't get it to work.

I have tried thinking it of as a complex curve integral

with

and trying to use a different parametrization for

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- Sep 30th 2010, 04:22 PMlusheslewisDefinite Integral, infinite limits, complex analysis
I need to show that:

It seems obvious that i need to use

but I can't get it to work.

I have tried thinking it of as a complex curve integral

with

and trying to use a different parametrization for - Sep 30th 2010, 04:30 PMAckbeet
I'd be willing to bet that you could take the RHS, substitute exp(ix) = cos(x) + i sin(x), and then use properties of even and odd functions to get the desired result. Are you sure that that -1 is in the numerator of the RHS's integrand? Because that's not such a nice feature of the problem.

- Sep 30th 2010, 04:34 PMlusheslewis
Yes, the -1 is definitely there. It is straight out of the book.

Maybe it has something to do with the limit of as x -> 0

Edit: Your idea does seem to work since is odd and should integrate to zero. I was trying to go from the left and show it equals the right though which was obviously the wrong way. Cheers! - Sep 30th 2010, 05:17 PMAckbeet
Glad you got it to work. Have a good one!