How do I evaluate gaussian integrals with positive, real constants?

[agingstudent]

Homework Statement

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 pi^1/2 but I don't know how to relate that to this equation. My guess is the integral is Api^1/2but 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.

The Attempt at a Solution

 

[gabbagabbahey]

Try a simple u-substitution, [itex]u=\sqrt{m}(x-a)[/itex]...