# Changing the Gaussian Distribution from cartesian to polar coordinates

1. Mar 27, 2013

### stepheckert

1. The problem statement, all variables and given/known data
"You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine the integrands and turn the area integral, over x and y into an area integral over polar coordinates.

3. The attempt at a solution
The back of the book has this answer:
1=A^2Integral(e^(-B(x^2+y^2)dxdy)=A^2Integral((e^-Br^2)(r)drdθ)=PiA^2/B.

I understand the first piece but I don't understand how to get from these cartesian to polar coordinates at all, and I'm very confused as to how they got the final answer from the last integral.