FIGURE N7–12
The volume ΔV of a typical disk is given by ΔV = π y^2 Δx. The equation of the circle is x^2 + y^2 =
r^2. To find the volume of the sphere, we form a Riemann sum whose limit as n becomes infinite is a
definite integral. Then,
EXAMPLE 7
Find the volume of the solid generated when the region bounded by y = x^2 , x = 2, and y = 0 is rotated
about the line x = 2 as shown in Figure N7–13.
SOLUTION:
Disk.FIGURE N7–13
See Questions 18, 49, 51, 52, and 53 in the Practice Exercises for examples of finding volumes by