Question

For Calculus, when calculating the volume of revolutions (volume of disk or washer method), how to know which one to use?

Answer 1

if i ended up findin inverse of a function ( like y=x^3+x^2+x
+1) i would look for another method ...

Answer 2

so it depends on the function
all of them will give you th same result.

Answer 3

How do you know which method is better?
Washers or Shells?

It comes down to which one is easier to integrate.
So sometimes you won't know which method is easier until you've set up the integral. That can be a little annoying since most of the effort goes into set up for these solids of revolution. :)

Answer 4

And just so it's clear,
you'll never choose between a disk and a washer.

One direction will give you a shell,
the other direction will give you a disk or washer.

A washer is just a disk, but with a hole in it.

Answer 5

To avoid confusion:

As to whether you use disk or washer,
use disk when the axis of rotation 'covers' the the curve of interest
use washer when the axis of rotation is outside of the curve. you will have a 'hole'
These are exclusive so you can never use both.



Shells is an entirely different approach.