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

Using the disc/washer method.

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: 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.