The curve is  and .

Definition of surface area:

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

The curve is .

Apply derivative on each side with respect to .

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

Simpsons rule :

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Consider .

In this case .

Width .

Substitute and .

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Find the function values.

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Simpsons rule :

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Using Simpsons Rule, .

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

Using calculator, the value of the integral is .

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