Volumes of Rotating Functions: Shell vs. Washer Method

[Miike012]

Is there a general rule when to use the shell or washer method when working with calculating volumes of functions rotating about an axis? For instance should I use the shell method when rotating about the y-axis and use the washer method when rotating about the x?

 

[SammyS]

Is there a general rule when to use the shell or washer method when working with calculating volumes of functions rotating about an axis? For instance should I use the shell method when rotating about the y-axis and use the washer method when rotating about the x?

There is no general rule for this.

It's mostly a matter of convenience. Some regions to be rotated lend themselves to one method or the other.

 

[genericusrnme]

There's never any 'rule' for any problem, there are tools, there are definitions, there are conventions and there are conveniences but no rules (as long as everything follows from everything previous of course).

Usually it'd be more convenient to use the shell method for a volume below f(r) and the disk method for a volume above f(r).