Finding the Normalization Constant of a Gaussian Distribution (Griffiths 1.6)

[ADCooper]

Homework Statement

Consider the Gaussian Distribution

$ρ(x) = A e^{-λ(x-a)^{2}}$

where A, a, and λ are constants. Determine the normalization constant A.

Homework Equations

$\int^{∞}_{-∞}ρ(x) dx = 1$

The Attempt at a Solution

The problem recommends you look up all necessary integrals, so I did and I think that I've got it correct. I found that $A = \sqrt{\frac{λ}{π}}$. My question, if this answer is correct, is just: how do you do this integral? Do you have to actually do some kind of change of variables to a different coordinate system?

 

[TSny]

See here

 

[ADCooper]

See here

Thanks a bunch. I was a little confused because the solution I had found involved erf and I wasn't quite sure how to use it since I'd never seen that function before.