Finding Volume of Solid Using Disc/Washer Method for Rotation about the Y-Axis

[ParoXsitiC]

Homework Statement

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.

Homework Equations

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

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

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.

 

[SammyS]

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.

 

[ParoXsitiC]

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.

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