Find the area of the surface generated by revolving the curve about the indicated axis.
$y = \frac{1}{18}(x^2+1), 0 \le x \le \sqrt{17}$, y-axis
First set up the integral that gives the area of the given surface. Select the correct choice below and fill in the answer boxes to complete your choice.
(Type exact answers, using $\pi$ as needed.)
A. $S = \int_0^{\square} \square dx$
B. $S = \int_{\frac{1}{18}}^{\square} \square dy$
Now find the area of the surface S.
S = $\square$ square units (Type an exact answer, using $\pi$ as needed.)