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

1. Feb 2, 2010

### darkblue

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

S=integral from a to b x 2pix ds where ds=sqrt(1+(dy/dx)2)dx

3. 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?

2. Feb 2, 2010

### Staff: Mentor

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

3. Feb 2, 2010

### darkblue

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.

4. Feb 2, 2010

### Staff: 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?

5. Feb 2, 2010

### darkblue

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