FIGURE N7–28
SOLUTION:
About the y-axis.
Shell.
ΔV = 2πxy Δx = 2π Δx.
Note that diverges to infinity.Chapter Summary
In this chapter, we have reviewed how to find areas and volumes using definite integrals. We’ve
looked at area under a curve and between two curves. We’ve reviewed volumes of solids with
known cross sections, and the methods of disks and washers for finding volumes of solids of
revolution.
For BC Calculus students, we’ve applied these techniques to parametrically defined functions and
polar curves and added methods for finding lengths of arc. We’ve also looked at improper integrals
and tests for determining convergence and divergence.
‡No question requiring the use of shells will appear on the AP exam.
Practice Exercises
Part A. Directions: Answer these questions without using your calculator.
AREA
In Questions 1–11, choose the alternative that gives the area of the region whose boundaries are
given.