I have $r = \sqrt{\theta}$
http://www.wolframalpha.com/input/?i=cartesian+r+%3D+%5Csqrt%7Btheta%7D+
The graph given in the book ends at the first time it approaches to right side of the x axis (or 2pi). I attempted to set up an integral that cut each section of the graph so I have 4 section to compute that integral in and it did not even give close to the correct answer ($\pi^2$).
I tried to do
$\int_0^ {\pi/2} \sqrt {\theta} d \theta$ $\int_{\pi/2}^ {\pi} \sqrt {\theta} d \theta$ $\int_\pi^ {3\pi/2} \sqrt {\theta} d \theta$ $\int_{3\pi/2}^ {2\pi} \sqrt {\theta} d \theta$
This basically gives me just the integral of $\frac{1}{4} \theta^{2}$ evaluated $2\pi$ since everything else cancels out.