$\"\"$

The function is $\"\"$ .

The region $\"\"$ is rotated about the $\"\"$ -axis.

The differential of arc length : $\"\"$ .

Consider $\"\"$ .

Differentiate with respect to $\"\"$ .

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Surface area of the curve when rotated about $\"\"$ -axis : $\"\"$ .

Substitute $\"\"$ in the above formula.

$\"\"$

Thus, the surface area is infinite.

$\"\"$

The surface area is infinite.