## Calculus: Early Transcendentals 8th Edition

$$S=\left\{(x, y) | 0 \leq x \lt \pi / 2, \quad 0 \leq y \leq \sec ^{2} x\right\}$$ 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
$$S=\left\{(x, y) | 0 \leq x \lt \pi / 2, \quad 0 \leq y \leq \sec ^{2} x\right\}$$ 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