# Thread: volume of a solid of revolution?

1. ## 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?

2. 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,
$\pi \int_{-1}^1 (x^4-1)^2 dx$

3. Well, that's what I thought too, but apparently my answer is wrong.
Came out to 4.4680?

4. Try using shells.

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