I am trying to learn the proof for the value of the Gaussian Integral posted here: Gaussian integral - Wikipedia, the free encyclopedia
under 'By Cartesian Coordinates"
I understand the basics of double integration, but I don't quite understand this proof.
I see that the function is an even function...but what is the significance of saying "Let x=ys and dy=xds"
I also cannot see how
And...I also do not understand how the 's' variable arises later on into the proof.
I would greatly appreciate if these questions were answered and it would be extremely appreciated if a quick run through of this proof was posted.
Thank you very much.