# Volume of revolution

• April 5th 2009, 06:32 PM
Shyam
Volume 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.
• April 5th 2009, 06:37 PM
Jhevon
Quote:

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

did you sketch the region? we employ the disk (washer) method here. note that the inner radius $r$ is 3, while the outer radius $R$ is $3 - (x - 4)(x - 2) = 6x - x^2 -5$

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