# Homework Help: Help with an Integral

1. Jan 21, 2006

### eep

Hi,
I'm having problems integrating the following function:
$$\int^\infty_{-\infty}Ae^{-\lambda(x - a)^2}$$
Where A, $\lambda$, and a are positive, real constants. If anyone could point me in the right direction I'd really appreciate it.

The integral is supposed to be equal to 1 and using that fact I'm supposed to solve for A. This is from Griffiths' Quantum Mechanics Chapter 1.

Last edited: Jan 21, 2006
2. Jan 21, 2006

### StatusX

You can do the substitution u=x-a (you shouldn't actually have to do that, just think about what it would do), and then use the fact that:

$$\int_{-\infty}^{\infty} e^{-a x^2} dx = \sqrt{\frac{\pi}{a}}}$$

That's something worth memorizing, but you can derive it using the technique shown on http://en.wikipedia.org/wiki/Gaussian_function" [Broken] page.

Last edited by a moderator: May 2, 2017
3. Jan 22, 2006

### eep

Thank you! So assuming I made the correct substitutions and such I end up with the integral being equal to:

$$A\sqrt{\frac{\pi}{\lambda}}$$

And since the integral is equal to 1 (it's a probability thing)

$$A = \sqrt{\frac{\lambda}{\pi}}$$