# Integration using exponentials 2

1. Oct 17, 2012

### g.lemaitre

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

For this forum they use the following integration:

3. The attempt at a solution

Where does (u+a) come from? In step 2 why does the side on the left of the plus sign become zero? In step 3, how does A(0+a√π/λ) = a

This website likes you to work on problems but I can't work on something for which step 1 is a mystery.

2. Oct 17, 2012

### clamtrox

They do a change of variables, x-a = u, so x= u+a

The easiest way to see this is to notice that the integrand is an odd function (that is, f(-x) = -f(x)) and therefore the integral over an even interval [-n,n] is zero.

Did they calculate the value for A before? What you are doing here is calculating an expectation value of a random variable, so it should be true that
$$\int_{-\infty}^\infty dx Ae^{-\lambda(x-a)^2} dx = 1$$

Yes but you can't explain every single operation you do. It just seems to me you're trying to do assignments which are a bit too difficult for you. Maybe start from something easier?

3. Oct 17, 2012