# Homework Help: 2 part washer method?

1. Oct 11, 2011

### ParoXsitiC

1. The problem statement, all variables and given/known data

I need to find the volume of the solid formed when rotating f(x) = 4x-x^2 and y=4 and x=0 about the y-axis.

Using the disc/washer method.

2. Relevant equations

v = pi * integral from a to b of (r^2) * thickness

3. The attempt at a solution

I already did it using the shell method and got 128/3 pi.

I am getting confused on how to do this, I believe it will need to be setup in 2 parts? Refer to my image sketch:

[PLAIN]http://k.minus.com/je3SvPydQUFsp.png [Broken]

Where I think the 2 parts are split by x=2. From x=0 to x=2 I see a disc method and then from x =2 to x=4 I see the washer method. However because the disc/washer method is perpendicular to the axis of rotation (y) that means that the thicknes of the disc/washers will be dy, which means the limits of integration would be in terms of y. Therefore I don't see how I can set it up with 2 equations with different integrals.

Last edited by a moderator: May 5, 2017
2. Oct 11, 2011

### SammyS

Staff Emeritus
The volume is formed by rotation about the x-axis. The disks/washers should be vertical, not horizontal.

They should be washers for this problem.

3. Oct 12, 2011

### ParoXsitiC

Sorry it is about the y-axis , it was a mistype in the question on my part.