Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve y=xe-x 1=<x=<3 about the y-axis.
S=integral from a to b x 2pix ds where ds=sqrt(1+(dy/dx)2)dx
The Attempt at a Solution
The first thing I tried to do is solve for the equation in terms of x, and then use the equation above. I figured it makes sense to solve for x since we are rotating the curve about the y-axis. I wasn't able to solve for x, so then I tried to use this method in my textbook where you leave x as it is, and then substitute u for whatever is within the square root sign in such a way that you can eliminate x. I tried to do that, but its turning into a mess since you get 1+(e-x-xe-x)2 underneath the square root and I don't really see how substitution could be used here...any ideas?