Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x - axis.

Answer 1

Step 1:

The equations are and .

The volume of the solid generated revolving about the - axis.

Washer method:

The outer radius of revolution is .

The inner radius of revolution is .

Substitute and in .

Integrate between 0 and 1.

Step 2:

Solve the integral by using substitution method.

Apply derivative on each side with respect to .

Substitute and in .

Apply formula .

Back substitute .

.

The volume of solid is cubic units.

Solution:

The volume of solid is cubic units.