Barrons AP Calculus - David Bock

(Note that we obtained the same result using disks in Example 7.)
FIGURE N7–18

EXAMPLE 11
The region bounded by y = 3x − x^2 and y = x is rotated about the y-axis. Find the volume of the solid
obtained. See Figure N7–19.

SOLUTION:

About the y-axis.

Shell.

FIGURE N7–19

EXAMPLE 12

Find the volume obtained when the region bounded by y = x^2 and y = 2x is revolved about the x-axis.
SOLUTION: The curves intersect at the origin and at (2,4), as shown in Figure N7–20. Note that
we distinguish between the two functions by letting (x 1 , y) be a point on the line and (x 2 , y) be a
point on the parabola.