# Volume by cylindrical shells

• September 9th 2008, 11:46 AM
fogel1497
Volume by cylindrical shells
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!
• September 9th 2008, 03:42 PM
skeeter
radius of a representative cylindrical shell is $x$, not $31e^x$.

$V = 2\pi \int_0^1 x(31e^x - 31e^{-x}) \, dx$