Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.8 - Improper Integrals - 7.8 Exercises - Page 535: 45

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
1566358015

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
Small 1566358015
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.