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

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

tkhunny · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Nevermind I got it! Thank you!