1. The problem statement, all variables and given/known data Compute the region R in the first quadrant between y=e^(-x), x=0, and y=0. Compute using shells, the volume V of solid around the y-axis. 2. Relevant equations Volume =integral of bounds 2pi*radius*height 3. The attempt at a solution First I drew the graph. This graph really is just a graph of e^(-x). I then visually rotated it around the y-axis. This problem seems easy enough to set up: Volume = Integral between 0 (lower limit) and infinity (upper limit) of 2*pi*x*e^-(x) dx where x = radius dx = width e^(-x) = height This problem was also easy to integrate using integral substitution first, and then integration by parts one time. The final equation was V = 2pi[-xe^(-x)-e^(-x)] from 0 to infinity. After calculating the simple answer is 2pi. My problem: For some reason, when I use this calculator: http://www.wolframalpha.com/widgets/view.jsp?id=1cd73be1e256a7405516501e94e892ac I get an answer of pi/2. Am I doing something wrong? Or is my answer/thinking correct? Thank you.