Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.

The region bounded by f(x)= (x + 1)−3 and the x-axis on the interval [0, ∞) is revolved about the y-axis.

Problem 24E

Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.

The region bounded by and the x-axis on the interval [0, ∞) is revolved about the y-axis.

Solution

Step 1

In this problem we have to find the volume of the described solid of revolution or state that it does not exist.

We shall find the volume by using the following 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 ”