Cracking The Ap Calculus ab Exam 2018

If you were to slice the region vertically, you would use washers. You’ll need to add 3 to each radius to
adjust for the axis of revolution. The integral to evaluate is

π [(16  −   x^2     +   3)^2    −   (16 −   4x  +   3)^2 ]  dx

To slice the region horizontally, use cylindrical shells. The radius of each shell would increase by 3, and
you would evaluate

PROBLEM 6. Repeat Problem 1, but revolve the region about the line x = 8. You may use either method.
Set up but do not evaluate the integral.

Warning! This one is tricky!

Answer: First, sketch the region.