Cracking The Ap Calculus ab Exam 2018

looks like the following:

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

PROBLEM 2. Repeat Problem 1, but revolve the region about the y-axis and use the cylindrical shells
method. Set up but do not evaluate the integral.

Answer: Sketch the situation.

Slicing vertically, the top of each cylinder is y = 16 − x^2 , the bottom is y = 16 − 4x, and the radius is x.
Therefore, you should set up the following:

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

PROBLEM 3. Repeat Problem 1 but revolve the region about the x-axis and use the cylindrical shells
method. Set up but do not evaluate the integral.

Answer: Sketch the situation.