Changing the Gaussian Distribution from cartesian to polar coordinates

[stepheckert]

Homework Statement

"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.

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.

Please Help!
Thanks!

 

[vela]

You should review changing coordinates, which was covered in your calculus course.