Find the volume generated by the rotation of the region bounded by y = (x-4)(x-2) and y = 0 about y = 3.

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- Apr 5th 2009, 06:32 PMShyamVolume of revolution
Find the volume generated by the rotation of the region bounded by y = (x-4)(x-2) and y = 0 about y = 3.

- Apr 5th 2009, 06:37 PMJhevon
did you sketch the region? we employ the disk (washer) method here. note that the inner radius $\displaystyle r$ is 3, while the outer radius $\displaystyle R$ is $\displaystyle 3 - (x - 4)(x - 2) = 6x - x^2 -5 $

the volume of revolution is given by $\displaystyle V = \pi \int_2^4 (R^2 - r^2) ~dx$