# * * (Exam tomorrow morning!)

1. Jun 20, 2011

### L-x

*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) $$2.pi.i (\frac{1}{2.2^{1/2}}(1+i) + \frac{1}{2.2^{1/2}}(1-i))$$

$$= 2.i.pi.2^{1/2)}$$

I have used I to 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 is I and from the line just below the real axis is -I*exp(i.pi)=I, so we end up with I = 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 to I please?

Last edited: Jun 20, 2011
2. Jun 20, 2011

### Dick

Re: *URGENT* (Exam tomorrow morning!)

I don't think your residue calculation for the contour is correct. When I do it I get a different answer that doesn't have an i in it. Can you show your steps?