# more volume of resulting solid

• Aug 7th 2009, 11:43 AM
dat1611
more volume of resulting solid
The region between the graphs of y=x2 and y=2x is rotated around the line x=2.
The volume of the resulting solid is

ok i need some more help with this one

|2
| pi[(2-x^2)^2-(2-2x)^2]
|0

im not sure what im doing wrong here
• Aug 7th 2009, 11:56 AM
skeeter
Quote:

Originally Posted by dat1611
The region between the graphs of y=x2 and y=2x is rotated around the line x=2.
The volume of the resulting solid is

ok i need some more help with this one

|2
| pi[(2-x^2)^2-(2-2x)^2]
|0

im not sure what im doing wrong here

you have to use cylindrical shells w/r to x ...

$V = 2\pi \int_0^2 (2-x)(2x-x^2) \, dx$

... or washers w/r to y.

$V = \pi \int_0^4 \left(2-\frac{y}{2}\right)^2 - (2-\sqrt{y})^2 \, dx$