1. The problem statement, all variables and given/known data This is not a homework problem per se, I'm just reviewing old material for my upcoming final examination in my calculus course and find improper integrals are a weak point of mine. I've picked a fairly simple example that I'm having problems grasping. It is the integral from -infinity to 0 of [tex]\int(xe^-x^2) dx[/tex] (I'm sorry I don't really know how to use Latex properly.) 3. The attempt at a solution Well, I undertand that after we evaluate the integral, we get the limit as t--> -infinity [-1/2 + 1/2e^(-t^2)] Now, I already know the answer will come out to -1/2, therefore making the second limit convergent and equal to 0. Why is this? I think I'm getting confused trying to square -infinity, then take the negative of THAT, then raise e to that number. I'm very confused here, is there an easy way to look at these problems? I try to look at the graph in my head, but that always ends up giving me the wrong answer. Any tips for how to attack these problems would be very much appreciated.