jasonbay74
New member
- Joined
- Mar 31, 2013
- Messages
- 2
Calculate the volume of the solid of revolution formed by rotating the region around the y-axis. Apply the shell method.
f(x)=e^x, x=0, y=8
This is what I did: (I integrated from 0 to 8)
V=∫ 2πx(8-e^x)dx
=2π∫ (8x-xe^x)
I used integration by parts with u=x, du=1dx, v=e^x, and dv e^x(dx)
giving:
2π[8∫ xdx-(xe^x-∫ e^x(dx)]
my final answer was -129507.1677
When I apply the disk method using x=ln(y) I get 48.13407626.
These two answers should be the same and I think there's an error in my shell method that I can't figure out???
f(x)=e^x, x=0, y=8
This is what I did: (I integrated from 0 to 8)
V=∫ 2πx(8-e^x)dx
=2π∫ (8x-xe^x)
I used integration by parts with u=x, du=1dx, v=e^x, and dv e^x(dx)
giving:
2π[8∫ xdx-(xe^x-∫ e^x(dx)]
my final answer was -129507.1677
When I apply the disk method using x=ln(y) I get 48.13407626.
These two answers should be the same and I think there's an error in my shell method that I can't figure out???