volume of resulting solid

• Aug 7th 2009, 10:52 AM
dat1611
volume of resulting solid
The region between the graphs of y=x^2 and y=4x is rotated around the line y=16.
The volume of the resulting solid is

i thought it would be the definite integral

|16
| pi[((x^2)^2)-((4x)^2)]dx
|0

but thats not right
• Aug 7th 2009, 11:14 AM
skeeter
Quote:

Originally Posted by dat1611
The region between the graphs of y=x^2 and y=4x is rotated around the line y=16.
The volume of the resulting solid is

i thought it would be the definite integral

|16
| pi[((x^2)^2)-((4x)^2)]dx
|0

but thats not right

did you make a sketch?

$V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx$

$R(x) = 16-x^2
$

$r(x) = 16-4x$

limits of integration are from $a = 0$ to $b = 4$