Question

The solid lies between planes perpendicular to the x axis at x = −1 and x = 1. The
cross sections perpendicular to the x axis are circular disks whose diameters run from the
parabola y = x
2
to the parabola y = 2 − x
2
. Find the volumes of the solid.

Answer 1

Answer: 352/105

Step-by-step explanation:

Diameter of the circular disk is

(2−x2)−x2

so that the radius of the disk is the diameter divide by 2

(2−x2−x2)/2.

Integrating V at 1 and -1, we get

V =Z 1−1A dx =Z 1−1π(1 − x2)2

dx = π(x −2/3x3 +1/5x5)1−1

=16/15π

= 352/105