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.

Question

Mathematics

Guest

26 March, 21:35

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.

+4

Answers (1)

Know the Answer?

Benjamin · 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

The solid lies between planes perpendicular to the x axis at x = - 1 and x = 1. Thecross sections perpendicular to the x axis are circular disks whose diameters run from theparabola y = x2to the parabola y = 2 - x2. Find the volumes of the solid.

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.