Volumes of solids

Find the volume of the following solids.

The region bounded by y = 1/(x + 2), y = 0, x = 0, and x = 3 is revolved about the line x = −1.

Problem 47E

Volumes of solids Find the volume of the following solids.

The region bounded by , y = 0, x = 0, and x = 3 is revolved about the line .

Solution

Step 1

In this problem we have to find the volume of the solid bounded by the region , y = 0, x = 0, and x = 3 is revolved about the line .

We shall use shell method to find the volume.

Shell method : If R is the region under the curve y = f(x) on the interval [a, b], then the volume of the solid obtained by revolving R about the y-axis is