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 N7–19Example 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.
Shell.