$\"\"$

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 is,

$\"\"$

Therefore, 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 $\"\"$ .