# Integration Volume

1. Sep 29, 2007

there are the two types of volume integration which i am aware of, disc-integration and shell integration. What is the difference between these? where would each one? Also i was looking at shell integration on carious sites on the net, and i am still a little confused how the generic formula works. Could someone ever so kindly explain this to me?

many thanks,

2. Sep 29, 2007

### Staff: Mentor

The difference between disk and shell integration is where the axis of rotation is. Lets assume that you are integrating a solid of rotation of some f(x)dx. If the axis of rotation is parallel to the x axis then you use disk integration, but if the axis of rotation is perpendicular to the x axis then you use shell integration.

3. Sep 29, 2007

### chaoseverlasting

How would you find the general vector equation of a solid of revolution?

4. Sep 29, 2007

### HallsofIvy

Staff Emeritus
"Disks" works, of course, by using disks- normally, the radius of the disk is the value of the function and you calculate the area by $\pi f(x)$, multiply by the "thickness", dx, and then integrate.

"Shells" works by using thin cylinders. The radius is typically the x-value so you have a "circumference" calculation $2\pi x$ and then multiply by the "height" of the cylinder, f(x): you integrate [itex]2\pi x f(x) dx[/itex\.

5. Sep 29, 2007