I want to convert
$$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\int_1^{\csc{\theta}}r^2\cos{\theta}drd\theta$$
into Cartesian coordinates.
I understand that $r\cos{\theta}=x$ and $rdrd\theta=dxdy$.
But how can I convert the upper limits and the lower limits?
I tried to use
$$\pi/6 \le f(r,\theta)$$
But it seems I can't find the upper limit since it is the function.
I know how to convert from Cartesian to polar.
But when it comes to polar to Cartesian, I am not sure how to draw that $r=\csc{\theta}$ in polar plane.