Step 1:

The function is and .

Definition:

If the curve is described as , then the surface area of the curve obtained by rotating about the -axis is

The curve is .

Differentiate on each side.

Area of the surface obtained by the curve rotating about the -axis is

Step 2:

Simpsons rule :

Let be continuous on and let be an even integer,

The Simpsons Rule for approximating is given by,

where and

Using Simpson Rule, .

Step 3:

Area of the surface obtained by the curve rotating about the -axis is

Using calculator, the value of the integral is .

Solution :

Using Simpson Rule, .