Question

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y - axis.

Answer 1

Step 1:

Disk method:

The curve equation is .

Vertical axis of revolution.

Formula for the volume of solid with the disk method, .

Solve for .

.

Step 2:

In this case .

From the graph, integral limits are .

Volume of the solid is

cubic units.

Solution:

cubic units.