$I=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \mathrm{~d} \theta \int_0^{\frac{1}{\sin \theta}} f(r) r \mathrm{~d} r=$
$\text{A.}$ $\int_0^1 \mathrm{~d} x \int_0^1 f\left(\sqrt{x^2+y^2}\right) \mathrm{d} y$.
$\text{B.}$ $\int_0^1 \mathrm{~d} x \int_1^x f\left(\sqrt{x^2+y^2}\right) \mathrm{d} y$.
$\text{C.}$ $\int_0^1 \mathrm{~d} r \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} f(r) r \mathrm{~d} \theta+\int_1^{\sqrt{2}} \mathrm{~d} r \int_{\frac{\pi}{4}}^{\arcsin \frac{1}{r}} f(r) r \mathrm{~d} \theta$.
$\text{D.}$ $\int_0^{\sqrt{2}} \mathrm{~d} r \int_{\arcsin \frac{1}{r}}^{\frac{\pi}{4}} f(r) \mathrm{d} \theta$.