Answer
$$
S=\left\{(x, y) | 0 \leq x \lt \pi / 2, \quad 0 \leq y \leq \sec ^{2} x\right\}
$$
The shaded area is the region of interest.
$$
\begin{aligned} \text { Area } &=\int_{0}^{\pi / 2} \sec ^{2} x d x\\
&= \infty. \end{aligned}
$$
Infinite area
Work Step by Step
$$
S=\left\{(x, y) | 0 \leq x \lt \pi / 2, \quad 0 \leq y \leq \sec ^{2} x\right\}
$$
The shaded area is the region of interest.
$$
\begin{aligned} \text { Area } &=\int_{0}^{\pi / 2} \sec ^{2} x d x\\
&=\lim _{t \rightarrow(\pi / 2)-} \int_{0}^{t} \sec ^{2} x d x \\
&=\lim _{t \rightarrow(\pi / 2)-}[\tan x]_{0}^{t}
\\
&= \lim _{t \rightarrow(\pi / 2)^{-}}(\tan t-0)\\
&= \infty. \end{aligned}
$$
Infinite area