Find the volume generated by revolving the area bounded by x=y^2 and x=4 about the line y=2.

Is it the integral from 0 to 4 of pi(4-(2-sqrt x)^2)?

Sorry I don't know how to use latex yet.

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- Nov 19th 2008, 11:13 AMelitespartWasher method
Find the volume generated by revolving the area bounded by x=y^2 and x=4 about the line y=2.

Is it the integral from 0 to 4 of pi(4-(2-sqrt x)^2)?

Sorry I don't know how to use latex yet. - Nov 19th 2008, 01:52 PMskeeter
washer method ...

$\displaystyle R = 2 + \sqrt{x}$

$\displaystyle r = 2 - \sqrt{x}$

$\displaystyle R^2 - r^2 = (4 + 4\sqrt{x} + x) - (4 - 4\sqrt{x} + x) = 8\sqrt{x}$

$\displaystyle V = \pi \int_0^4 8\sqrt{x} \, dx$ - Nov 19th 2008, 02:32 PMgalactus
For shells, see if you get the same solution.

$\displaystyle 2{\pi}\int_{0}^{4}(y-2)y^{2}dy$ - Nov 19th 2008, 04:13 PMelitespart