Chapter 6.6, Problem 34E

Challenging surface area calculations Find the area of the surface generated when the given curve s revolved about the given axis.

34.     $y=\frac{1}{2}\ln \left(2x+\sqrt{4x^2-1}\right)$ between the points $\left(\frac{1}{2},0\right)$ and $\left(\frac{17}{16},\ln 2\right)$; about the y-axis