The function is and . \

Definition of surface area:

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

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The curve is .

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Differentiate on each side.

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

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Step 2:

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Simpsons Rule:

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Let  be continuous on . The Midpoint Rule for approximating  is given by

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where  and

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Using Simpson Rule, .

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Step 3:

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

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Using calculator, the value of the integral is .

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Solution:

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

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