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Question

Answer 1

8).

Step 1 :

The curve equations are ,  and .

Cylindrical shells method :

The volume of the solid obtained by rotating about the -axis the region under the curve is

.

Find the point of intersections.

Substitute in .

Now integrate over the interval 0 to 4.

Step 2:

Consider .

Volume of the solid obtained by rotating about the -axis the region under the curve and   is

.

Solution:

The volume of the solid is .

Answer 2

(7)

Step 1:

The equations are and .

The volume of the solid generated revolving about the line .

Washer method:

.

The outer radius of revolution is .

The inner radius of revolution is .

Find the integral limits by equating two curve equations.

.

Step 2:

Substitute and and and in .

.

Solution:

The volume of solid is cubic units.