Originally Posted by

**tom@ballooncalculus** You're reading it as the volume of revolution of the shaded area, yes? In that case there should be mention at least of the line x = 4.

I get 32/3 pi from washers/discs as well as shells.

Your disc radius, i.e. the length of the strip in your pic, should be

$\displaystyle x = 2 - \sqrt{4 - y}$

and then the washer distance will be the same again. So you don't need to split it. Double $\displaystyle 2 - \sqrt{4 - y}$ is what you need to square before integrating with respect to y.