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−2 and the x-axis on the interval [1, ∞) is revolved about the x-axis.

Problem 21E

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−2 and the x-axis on the interval [1, ∞) is revolved about the x-axis.

Answer ;

Step-1;

In this problem we need to find the volume of the solid founded by rotating around in the region

In order to find the volume, we will be using the following condition.

If f is a function such that for all in the interval , then the volume of the solid generated by revolving, around the x axis, the region bounded by the graph of , the x axis (y = 0) and the vertical lines andis given by the integral

Volume

Step-2;

Now , we have to find out the volume of a solid the region bounded by f(x) = = and the x-axis on the interval [1 , is revolved about the x-axis.

Consider f(x) = =

Then the volume (V) is

The graph of f(x) = = is shown below

Then =...