Posted by Jessica on Tuesday, October 20, 2009 at 9:04pm.
The region between the graphs of y=x^2 and y=2x is rotated around the line x=2.
The volume of the resulting solid is ____. Please help. I've tried this problem so many times but i keep getting it wrong. I thought the outer radius would be (20) and inner radius is (2x^2) integrated from 0 to 2, but its not right.

calculus  Reiny, Tuesday, October 20, 2009 at 10:17pm
They intersect at (0,0) and (2,4)
Since you are rotationg about x = 2, we need to take horizontal slices and our
general formula will be
vol = pi(integral)(outer radius)^2  (inner radius)^2 dy from 0 to 4
Vol = pi(integral)((2y/2)^2  (2√y)^2)dy from 0 to 4
= pi[(1/12)y^3  (3/2)y^2 + (8/3)^(3/2)] from 0 to 4
My answer came out to be 8/3
Let me know if your text agrees.
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