Hi, I am having difficulty getting to the end with this one...see attached

Thanks

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- Nov 21st 2010, 03:37 AMbugatti79Tricky Gauss Integral problem
Hi, I am having difficulty getting to the end with this one...see attached

Thanks - Nov 22nd 2010, 10:30 PMChris L T521
Keep in mind that . (*)

I take it you mean the original problem is , because the 2m term appears out of nowhere in the second step.

For the moment, let's focus on the exponent:

.

Rearranging, we get

(Verify)

Complete the square to get

(Verify)

With this, we can now evaluate this integral instead:

Now apply the substitution .

Thus, the integral becomes

.

Now apply (*) to get

which appears to be different from the answer you have supplied....so maybe I made a mistake somewhere??

But this is the idea of how to approach this problem. Hope this helps! - Nov 22nd 2010, 10:33 PMbugatti79
- Nov 25th 2010, 10:24 AMbugatti79
- Nov 25th 2010, 11:02 AMChris L T521
- Nov 25th 2010, 01:32 PMbugatti79
- Nov 25th 2010, 01:43 PMChris L T521
As I said in my previous response, you need to have the coefficient of the term to be 1 in order to complete the square. Thats why I did the following:

Now that its in the proper form, we complete the square -- i.e. :

So when you go back to the integral in question, the substitution becomes

Then the rest of the problem becomes algebra once you apply the formula for the Gaussian.

Does this clarify things? - Nov 25th 2010, 02:56 PMbugatti79