Surface Area: y=e^(-x)

[highlightall]

I need to find the surface area of the shape formed when the infinite curve y=e^(-x), x>=0 is rotated around the x-axis. I set up the problem with the formula for surface area and attempt to integrate from 0 -> infinite, but the value seems to go without bound. I confirmed it in Mathematica, which is having a hard time with it.. so I must be doing something wrong with the set up.

Integrate( 2pi * e^(-x) * sqrt(1 + e^(-2x)) )


The author refers back to an example from another chapter as a "hint", but I am missing the link. The example has to do with integrating sec^3(x)dx. What does it have to do with this problem? What am I doing wrong?

 

[Unco]

Your setup in fine. Let e^(-x) = tan(u) and you'll see how the hint comes into play.

It's probably easiest to substitute back and use x limits.