#### Answer

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

#### Work Step by Step

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 $ACD$.