$\"\"$

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

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

$\"\"$ .

$\"\"$

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

$\"\"$

Substitute corresponding values in $\"\"$ .

$\"\"$

The surface area :

$\"\"$

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

$\"\"$

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