# volume of a solid of revolution?

• December 7th 2006, 08:19 PM
thedoge
volume of a solid of revolution?
hello. i am not quite sure how to solve these problems when they aren't revolving around the x or y axis. for example:

area within y=x^4 , y=1

revolving around y=8

What do I do?
• December 7th 2006, 08:46 PM
ThePerfectHacker
Quote:

Originally Posted by thedoge
hello. i am not quite sure how to solve these problems when they aren't revolving around the x or y axis. for example:

area within y=x^4 , y=1

Revolving $x^4$ about line $y=1$.

Is the same as revolving $x^4-1$ about the line $y=0$ (x-axis). Think of this as a picture.

Thus,
$\pi \int_{-1}^1 (x^4-1)^2 dx$
• December 7th 2006, 08:55 PM
thedoge
Well, that's what I thought too, but apparently my answer is wrong.
Came out to 4.4680?
• December 8th 2006, 04:06 AM
galactus
Try using shells.

$2{\pi}\int_{0}^{1}(x-8)(x^{4}-1)dx$