# Solid of revolution

8 videos

Using definite integration, we know how to find the area under a curve. But what about the volume of the 3-D shape generated by rotating a section of the curve about one of the axes (or any horizontal or vertical line for that matter). This in an older tutorial that is now covered in other tutorials.
This tutorial will give you a powerful tool and stretch your powers of 3-D visualization!

### Disc method: Function rotated about x-axis

VIDEO
10:05 minutes

Figuring out the volume of a function rotated about the x-axis.

### Disc method (rotating f(x) about x axis)

VIDEO
7:31 minutes

The volume of y=sqrt(x) between x=0 and x=1 rotated around x-axis

### Disc method with outer and inner function boundaries

VIDEO
8:22 minutes

More volumes around the x-axis.

### Shell method to rotate around y-axis

VIDEO
9:29 minutes

Use the "shell method" to rotate about the y-axis

### Disc method: Rotating x = f(y) around the y-axis

VIDEO
9:19 minutes

Using the disk method around the y-axis.

### Shell method around a non-axis line

VIDEO
10:06 minutes

Taking the revolution around something other than one of the axes.