# Setting up an Integral for the area of a surface of revolution

## Homework Statement

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.

## Homework Equations

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?

Mark44
Mentor
All you need to do is set up the integral. Don't worry about trying to evaluate this integral.

So does this mean that the way I have set it up is correct? I had a feeling it wasn't right because I couldn't see what steps I'd take next in the event that I had to solve it.

Mark44
Mentor
Seems to be OK, but I'm a little rusty on these surface area integrals. You have an extra x in what you typed, though, right after b. Did you mean for that to be there?
darkblue said:
S=integral from a to b x 2pix ds where ds=sqrt(1+(dy/dx)2)dx

oops, i meant to put a "*" for multiplication.