Gratuitously Polarized

Calculus Level 4

\[\begin{array} {} x = r \cos (\theta) \\ y=r \sin(\theta) \\ r = \sec(\theta) & \text{for } 0 \leq \theta \leq \frac{\pi}{4} \\ r = \csc(\theta)& \text{for } \frac{\pi}{4} < \theta \leq \frac{\pi}{2} \end{array} \]

The curve described above exists within the \(xy\) plane. Determine the area bounded by this curve, the \(x\)-axis, and the \(y\)-axis.

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