Cracking The Ap Calculus ab Exam 2018

To slice horizontally, you have to solve each equation for x in terms of y and find the limits of integration
with respect to y. First, solve for x in terms of y.

y   =   16  −   x^2     becomes x   =   

and

y   =   16  −   4x  becomes x   =   

Next, determine the limits of integration: They’re from y = 0 to y = 16. Slicing horizontally, the curve x =

    is  always  on  the right   and the curve   x   =       is  always  on  the left.   The radius  is  y,  so  we

evaluate

PROBLEM 4. Repeat Problem 1 but revolve the region about the y-axis and use the washers method. Set
up but do not evaluate the integral.

Answer: Sketch.