Solids of revolution - shell method

7 videos
1 skill
You want to rotate a function around a vertical line, but do all your integrating in terms of x and f(x), then the shell method is your new friend. It is similarly fantastic when you want to rotate around a horizontal line but integrate in terms of y.

Shell method for rotating around vertical line

VIDEO 5:33 minutes
Introducing the shell method for rotation around a vertical line.

Evaluating integral for shell method example

VIDEO 11:00 minutes
Evaluating the definite integral set up using the shell method

Shell method for rotating around horizontal line

VIDEO 7:15 minutes
Find the volume of a solid of revolution by rotating around the x-axis using the shell method

Shell method with two functions of x

VIDEO 4:12 minutes
Using the shell method to rotate around a vertical line.

Calculating integral with shell method

VIDEO 3:59 minutes
Evaluating integral set up with shell method for two functions.

Shell method with two functions of y

VIDEO 7:11 minutes
Stepping it up a notch, our solid is now defined in terms of two separate functions.

Volumes of solids of revolution by shells

PRACTICE PROBLEMS
Volumes of solids of revolution, shell method