1. The problem statement, all variables and given/known data Recall that the integral from -∞ to +∞ of e^(-x^2) is equal to the square root of Pi. Use this fact to calculate the double integral of e^-(x^2 + (x-y)^2 + y^2) dx over the entire region R2. 2. Relevant equations 3. The attempt at a solution I am not sure if it's even the right thing to do, but whats in the brackets simplifies to e^-(2x^2-2xy+2y^2) = e^(2xy-2x^2-2y^2) Now to do the inner integral first, I will integrate with respect to x I can use the propery of exponents to formt he integral from -∞ to +∞ of e^2xy * e^(-2x^2) * e^(-2y^2) since y is a constant I can pull e^(-2y^2) and integrate just e^2xy * e^(-x^2) However, this is where I get stuck... I try to integrate by parts but that only gives me a more complicated integral to do, so I don't know if it's the right way to go. Any suggestions?