Question

use method of cylindrical shells to find volume of solid obtained by rotating region bounded by curves about specified axis:

y= e^x, y=e^-x, x=1 about the y axis

Answer 1

Use \(2\pi rh dr\) as your model.

\(2\pi\int\limits_{0}^{1}x\left(e^{x}-e^{-x}\right)\;dx\)

Verify with washers, using \(\pi r^{2}dh\) as your model

\(\pi\int\limits_{1/e}^{1}1^{2} - (-ln(y))^{2}\;dy + \pi\int\limits_{1}^{e}1^{2} - (ln(y))^{2}\;dy\)

Sorry, these are just too compelling. Make sure you see where ALL of that comes from.

Answer 2

i got the setup right but i must not be integrating right. i used integration by parts

Answer 3

i'm getting 2pi (2e+ 2e^-1 -2)

Answer 4

Nevermind I got it! Thank you!