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I don't get what I did wrong in my work. Let me post it.

|dw:1358999196019:dw|

Did I set up the integral properly?

Let me send a pic.

I used the e points of intersection so I used 0 to 1.

x not e.

Ohh I can write in latex. It just takes too long lol.

It would have avoided much time and error.
7e-x is VERY different from 7e^(-x) or \(7e^{-x}\)

So I wrote my integral as:
\[14\pi \int\limits_{}^{}xe^x dx\]

How do I incorporate the e^-x then?

\(e^{x}\) is no good. You need \(e^{x} - e^{-x}\).

Huh? Why?

Nevermind. I see why.

The limits of intergation should still be the same right?

Did you draw a picture? The height of your cyllinders is the difference of the two curves.

Yeah I did, One moment.

|dw:1359002030111:dw|

Something like that.

That's it. And the final answer is?

I see why it's the difference though.

Sec.

\[\frac{ 28\pi }{ e}\] is what I got.

Eww... Natural logs...

No, no. It's far worse than that. :-)
When you are ready...

Ahh I see... Hehe...

Yeah... I have to use a calculator lol.