The integral is .

Consider the function is .

(a) Graph :

Graph the function  on .

(b) Sketch the volume of the integral using disk method.

Disk method :

The volume of the solid is .

The volume of the solid is .

Compare the two  integrals :

 and interval .

Graph :

Graph the function  and .

(c) Sketch the volume of the integral using shell method.

Shell method :

The volume of the solid is .

The volume of the solid is .

Compare the two  integrals :

 and interval .

Graph :

Graph the function  and .

(a)

(b)

(c)

.