# Evaluating gaussian integrals

1. Sep 7, 2009

### agingstudent

1. The problem statement, all variables and given/known data

The book says to consider the gaussian distribution

p(x) = Ae-m(x-a)2

where A, m, and a are all positive, real constants.

I have no idea how to evaluate this! The book says to look up the relevant integrals. I see the integral of e-x2is pi1/2 but I don't know how to relate that to this equation. My guess is the integral is Api1/2but I think m should appear somewhere in that equation.

I also need to find the average for x <x> and the average of x2<x2> BUT when I try to find this by evaluating the integral of xp(x) from infinity to negative infinity I just get 0, and that doesn't seem correct.

3. The attempt at a solution

2. Sep 8, 2009

### gabbagabbahey

Try a simple u-substitution, $u=\sqrt{m}(x-a)$....