# 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

Example showing how to find the volume of a solid of revolution (constructed by rotating around the x-axis) using the shell method (this could have been done with the disk method as well).

### 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

### Part 2 of shell method with 2 functions of y

VIDEO
5:11 minutes

### Volumes of solids of revolution by shells

PRACTICE PROBLEMS

Volumes of solids of revolution, shell method