How to apply the disk/washer and shell methods

[Steven_Scott]

In Calculus II, we're learning about solids of revolutions and computing their volumes.

I'm unsure when to apply the appropriate methods and how to make the correct partitions.
Please tell me if my reasoning is correct:

The disk/washer method is applied when your partitions are perpendicular to the axis of rotation and you use perpendicular partitions when your function is given by $$y = f(x)$$.

The shell method is used when the partitions are parallel to the axis of rotations and you use horizontal partitions when the functions is given by $$x = f(y)$$.

Is this correct?

Thanks!

Steven

 

[Mark44]

Is this correct?

Pretty much. Disks/washers are perpendicular to the axis of rotation, and shells are sort of parallel to it. Typically, either method can be used, but sometimes one technique leads to an easier integration.

Another way to look at it is that the thin dimension of a disk or washer is one subinterval in your partition, while the thickness of a shell is one subinterval. For a given axis of rotation, disks/washers will have a partition interval along one coordinate axis, and shells will have a partition interval along the other coordinate axis.