$\"\"$

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The curve is $\"\"$ and the interval is $\"\"$ .

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The surface area formula for rotation about the $\"\"$ -axis is $\"\"$ .

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$\"\"$ .

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Differentiate the curve with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute corresponding values in $\"\"$ .

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The surface area is

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The exact area of the surface by rotating the curve about the $\"\"$ -axis is $\"\"$ square units.

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$\"\"$

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The exact area of the surface by rotating the curve about the $\"\"$ -axis is $\"\"$ square units.