Hi. I have this problem.

a) Use the Residue Theorem to calculate

where

is the unit circle {

} and

is real with

.

Okay, this is my attempt. I found the roots of

and came up with

, and noticed that we can only use

, and i denote this as

(and

)

Thus by the residue theorem

b) Use this to calculate

So I write the integral by letting

and

and yields

and i use the previous answer, and I get

The main problem is...

c)

**What happens to your argument (and the values of the integrals) when ** ?

What did you just write here above?? Is it ? If so then you'll have to take , since the other

root is out of the zone bounded by the path of integration...

Tonio
I'm not entirely sure about this one. My guess is

will now be the simple pole, but when i rework it all out again, it comes to the same conclusion of

.. so i'm not sure please help.