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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

Volume of a sphere

VIDEO 8:59 minutes
Figuring out the equation for the volume of a sphere.

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.

Shell method around a non-axis line 2

VIDEO 4:15 minutes
The last part of the problem in part 7