Challenge Question:

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- May 11th 2010, 02:44 AMRandom VariableYet another integral challenge question
Challenge Question:

**Moderator editor:**Approved Challenge question. - May 11th 2010, 03:38 AMNonCommAlg
- May 11th 2010, 07:23 AMRandom Variable
NonCommAlg

So are you saying that this problem is way to easy?

Anyways, here's what I did (which sounds like exactly what you did):

let

then

- May 11th 2010, 08:44 AMNonCommAlg
well, first of all the intagrand is an even function and so we just need to find the integral over then by parts gets us somewhere that we only need to find as you showed yourself. to find the value of i didn't use contour integration:

let first note that and so:

on the other hand, thus with solving this simple differential equation gives us

and therefore - May 11th 2010, 09:18 AMRandom VariableQuote:

well, first of all the intagrand is an even function and so we just need to find the integral over http://www.mathhelpforum.com/math-he...dcac81a7-1.gif

Here's another approach:

switch the order of integration

(again I used contour integration)

- May 11th 2010, 09:43 AMNonCommAlg
it'd be nice to find an elementary proof of mine is not elementary yet because i used differentiating an integral with respect to a parameter.

- May 11th 2010, 10:26 AMRandom Variable
- May 11th 2010, 08:58 PMsimplependulum
Or take a look if you are free ...

Sub. in the second integral , we have

Not long later , we will find that the integral is equal to :

- May 11th 2010, 09:03 PMsimplependulum