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
and trying to use a different parametrization for
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.
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!