Example 1:Determine the surface area created by rotating the curve y = f(x) about the y axis a full revolution.
Solution: Since the revolution is about the y axis, we only need to find the coordinate of the curve. We proceed by identifying the differential length along the curve as
We then calculate as
Notice that the integral in the denominator is the total length of the curve. Now, using the theorem of Pappus and Guldinus, we find the surface area as
where in this case and . Thus, the surface area is found to be