1. The problem statement, all variables and given/known data We define the improper integral (over the entire plane R^2) I as a double integral [-inf,inf]x[-inf,inf] of e^-(x^2+y^2)dA as equal to the lim as a-> inf of the double integral under Da of e^-(x^2+y^2)dA where Da is the disk with the radius a and center at the origin. Show that the I (the original double integral) equals pi. Sorry, this is rather difficult to type. 2. Relevant equations Other than what I've said, I know that the equation of a disk is x^2 + y^2 = r^2 3. The attempt at a solution With what I was given, I was able to substitute (x^2 + y^2) with r^2 resulting in the double integral of e^-(r^2). I also found the domain of r to be between 0 and a, and guessed that theta would range from 0 to 2pi. The problem I run into here is how to integrate the function. I first integrated the function with respect to theta because I thought that would be easier, but if I do that, I get the double integral [0,a]x[0,2pi] which doesn't seem right because of the a. Even if it was right, I don't know how to integrate the function of e^-(r^2). Working backwards, I deduced that I need to get an r into the equation somehow so I could integrate the function, but I don't know where to pull the other r from.