Normalizatoin Constant and a Gaussian Integral.

Hello! I'm attempting to compute the normalization constant N for the following function . This is generally done by evaluating , where the limits of integration are -inf to +inf.

I can get this right up until the point where I need to make a u substitution.

making the substitution

This integral is only slightly more clear to me. It looks like a Gaussian integral, but, how do I go about solving it? Any help is much appreciated.

Re: Normalizatoin Constant and a Gaussian Integral.

I would actually make the subtitution

That should make the integral a more standard integral.

Re: Normalizatoin Constant and a Gaussian Integral.

So, that would yield: ?

Re: Normalizatoin Constant and a Gaussian Integral.

Quote:

Originally Posted by

**atomicpedals** So, that would yield:

?

I don't think you've quite got it yet. The substitution I suggested requires a change in the differential as well. The final answer had better have a 'k' in it somewhere.

Re: Normalizatoin Constant and a Gaussian Integral.

Woops! which then yeilds a normalization constant .

Re: Normalizatoin Constant and a Gaussian Integral.

Better, but still not quite there yet. Be careful as to numerator and denominator. Can you show your working, please?

Re: Normalizatoin Constant and a Gaussian Integral.

So my line of thinking was as follows:

which I think yields and so

Re: Normalizatoin Constant and a Gaussian Integral.

Wait... I should have shouldn't I...

Re: Normalizatoin Constant and a Gaussian Integral.

Quote:

Originally Posted by

**atomicpedals** So my line of thinking was as follows:

which I think yields

Fine so far.

Quote:

and so

The problem here is that what you start with is a dx, not a du. Solve du = dx/k for dx. That's what you must plug in.