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 $\displaystyle r$ 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 $\displaystyle V = \pi \int_2^4 (R^2 - r^2) ~dx$