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- Thread starter sonofjohn
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HallsofIvy

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First, of course, draw a picture. You should see that vertical line drawn from y= 2 will cross that region first at y= x and then at y= x

If you want to do it by "shells", each shell will be a thin cylinder of thickness dy, radius 2- y, and height [itex]\sqrt{y}- y[/itex]. The surface area of that will be [itex]2\pi(2- y)(\sqrt{y}- y)[/itex] and the volume will be [itex]2\pi(2- y)(\sqrt{y}- y)dy[/itex] integrated from y= 0 to y= 1.

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