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

[darkblue]

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]

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

 

[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.

 

[Mark44]

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?

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

 

[darkblue]

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

Thanks for your help!