## Calculus (3rd Edition)

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 $ACD$.