Just got back from my universities free tutoring sessions, and i think I have a pretty good grasp on this whole volume by cylindrical shells, (and pretty much every other shape). However I want to make sure I am doing these practice problems correctly so I don't get into a bad habit.

The problem is:

Consider the shape created by the lines y=31e^x , y=31e^(-x) , and x=1 revolved about the y-axis.

So what i setup was:

INTEGRAL of: (2pi)(r)(h)(dx)

I set r = 31e^x

h = 31e^x - 31e^(-x)

and then dx for the thickness

After you distribute terms i got INTEGRAL of: 2pi*31e^(x^2)

I pulled the 31 and 2pi out to get

62pi * INTEGRAL of: e^(x^2)

I solved for the integral and got e^(x^2)*(1/2x)

I evaluated that integral from 0-1 and got .5e

So my final answer was 31pi

On a side note, i have been looking for a 'how to' on how to use the math tags so i can make my expressions look all neat and what not, but can't seem to find it. I looked around different stickies, the faq, and the mathhelpwiki.

Thanks in advance to anyone who helps!