The curve is , where .

The differential of arc length : .

Consider .

Differentiate with respect to .

Substitute  in .

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

Substitute and in the above formula.

Let .

.

and

Substitute corresponding values in the above equation.

Let .

.

Substitute corresponding values in the above equation.

Consider . 

Integral reduction : .

Thus, . 

Substitute equation (2) in equation (1).

Substitute in the above equation.

Thus, the surface area is .

The surface area is .