The line equations are  , -axis, , and about -axis.

Method of disk:

The volume of the solid  is , where  is the cross sectional area of the solid .

.

Graph:

Radius .

Integral limits are and .

Power rule of integration: .

.

Volume of the solid is .

Solution:

Volume of the solid is .

Step 1:

The equations are  , -axis, , and about -axis.

Method of disk:

The volume of the solid  is , where  is the cross sectional area of the solid .

.

Graph:

Radius is .

Integral limits are and .

Integral formula: .

.

Volume of the solid is cubic units.

Solution:

Volume of the solid is cubic units.

The function is  and the inerval is .

Average value of the function on is defined as .

Here  .

Average value of is 

Power rule of integration: .

Average value of the function on is .

Consider .

Differentiate on each side with respect to .

.

Change of integral limits:

Lower limit: If then .

Upper limit: If then .

Substitute , and change of integral limits in .

. 

Average value of the function on is .

Average value of the function on is .