(adsbygoogle = window.adsbygoogle || []).push({}); *URGENT* (Exam tomorrow morning!) Calculating a real integral using residue theorem

1. The problem statement, all variables and given/known data

See attached picture

http://imageshack.us/photo/my-images/827/unledozs.jpg/

2. Relevant equations

3. The attempt at a solution

Parts a) and b) are straightforward.

For b) I end up with (using the residue theorem) [tex] 2.pi.i (\frac{1}{2.2^{1/2}}(1+i) + \frac{1}{2.2^{1/2}}(1-i)) [/tex]

[tex] = 2.i.pi.2^{1/2)}[/tex]

I have usedIto represent the real integral the question is asking us to evaluate.

for c), I can show that the contributions from the two circles on the contour are both 0, but the contributions from horizontal line just above the real axis isIand from the line just below the real axis is -I*exp(i.pi)=I, so we end up withI= i.pi/root(2). This is, of course, wrong: it is a real integral, it makes no sense for the answer we get to be imaginary. I'm certain my answer for b) is correct, so please could someone talk me through the procedure for relating the contour integral toIplease?

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# Homework Help: * * (Exam tomorrow morning!)

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