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The volume of the solid from the region bounded by $x=9-y^2$, $y=x-7$, $x=0$ about $y=3$ using cylindrical shells.

I've tried creating two separate regions:

$V_1=2\pi(3-y)(9-y^2)dy$ from 3 to 1

and

$V_2=2\pi(3-y)(y+7)dy$ from 1 to 0

but the answer this gives isn't correct. I can't seem to find any errors in my calculations. Am I devising the solution incorrectly?

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    Well, there are two different regions that those curves enclose: [see this diagram](http://i.stack.imgur.com/zDlMa.png). Do you mean the one above the $x$-axis, or the one below?2012-12-23
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    The question says x=0, so I'm assuming above it and also bounded by the y-axis. The textbook gives the answer as $369\pi/2$2012-12-23
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    Whoops, I misread the problem as referring to $y=0$, not $x=0$.2012-12-23
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    Ian, you can accept answers that you find particularly helpful. (You can upvote as many answers as you like, by clicking on the arrow above the "vote count" on the left of the answer, and can accept one answer per question by clicking on the "greyed out" check-mark to the left of that answer.2013-01-15

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