Barrons AP Calculus - David Bock

FIGURE N7–15

EXAMPLE 9

Find the volume of the solid generated when the region bounded by y = x^2 , x = 2, and y = 0 is rotated

about the y-axis, as shown in Figure N7–16.

SOLUTION:

Washer.

FIGURE N7–16
See Questions 19, 21, 48, 50, and 54 in the Practice Exercises for examples in which washers are
regarded as the differences of two disks.
Occasionally when more than one method is satisfactory we try to use the most efficient. In the
answers to each question in the Practice Exercises, a sketch is shown and the type and volume of a
typical element are given. The required volume is then found by letting the number of elements
become infinite and applying the Fundamental Theorem.
SHELLS‡