Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Preliminary Questions - Page 623: 3

The integral represents the area of the triangle $ACD$.

According to the figure, $\theta$ changes from $\pi/6$ (which is the angle between AC and the x-axis) to $\pi/2$ and $r=\csc \theta $ represents DC. Hence, the integral $$ \frac{1}{2} \int_{\pi / 6}^{\pi / 2} \csc ^{2} \theta d \theta $$ represents the area of the triangle $ACD$.