Thread: Volume about y axis

1. Volume about y axis

Find the volume of the solid formed by rotating the region enclosed by
, \ , \ , \
about the y-axis.

I'm just at a loss here as to how to proceed. It's a change about the y axis so I assume the functions have to be done with respect to y, but how can that be done for the first one, $y = e^x + 1$?

Any help on how to begin would be appreciated.

2. Originally Posted by Archduke01
Find the volume of the solid formed by rotating the region enclosed by
, \ , \ , \
about the y-axis.

I'm just at a loss here as to how to proceed. It's a change about the y axis so I assume the functions have to be done with respect to y, but how can that be done for the first one, $y = e^x + 1$?

Any help on how to begin would be appreciated.
use the method of cylindrical shells w/r to x ...

$V = 2\pi \int_0^{0.9} x(e^x + 1) \, dx$

... or use two integral expressions w/r to y.

$V = \pi \int_0^2 (0.9)^2 \, dx + \int_2^{e^{0.9}+1} (0.9)^2 - [\ln(y-1)]^2 \, dy$

3. Originally Posted by skeeter
use the method of cylindrical shells w/r to x ...

$V = 2\pi \int_0^{0.9} x(e^x + 1) \, dx$

... or use two integral expressions w/r to y.

$V = \pi \int_0^2 (0.9)^2 \, dx + \int_2^{e^{0.9}+1} (0.9)^2 - [\ln(y-1)]^2 \, dy$
Thank you. I think there was a way to find the integral of $x(e^x+1)$ by using substitution ... is this true, and how?

4. Originally Posted by Archduke01
Thank you. I think there was a way to find the integral of $x(e^x+1)$ by using substitution ... is this true, and how?
you would need to use the method of integration by parts.