1. The problem statement, all variables and given/known data ∫ e^([tex]\pi[/tex]x^2) dx, with limits -∞ to ∞ 2. Relevant equations ∫∫ dxdy = ∫∫ rdrdθ 3. The attempt at a solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^[tex]\pi[/tex](x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy Introduce polar coordinates: x^2 + y^2 = r^2 The equation becomes: ∫∫ e^([tex]\pi[/tex]r^2) rdrdθ But I don't know how to change the limits. Am I right in that the r limits stay the same and the θ limits change to [tex]\pi[/tex]/2 and -[tex]\pi[/tex]/2? If this is right, when I integrate the first part, I end up with 0. Is this correct? Thanks for any help. P.S. I don't know why the pi is higher than the other figures, but it's meant to be at the same level!