Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.2 Regions Between Curves - 6.2 Exercises - Page 417: 13

Answer

$\pi-2$

Work Step by Step

Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$ Thus, the area of the region is: $A=\int_a^b [f(x)-g(x)] \ dx= \int_{-1}^{1} [\dfrac{2}{1+x^2}-1] \ dx\\=[2 \arctan x-x]_{-1}^1 \\=2 \arctan (1)-1- [-2 \arctan (-1) -(-1)] \\=2\times \dfrac{\pi}{4}-1-[2(\dfrac{-\pi}{4})+1] \\=\pi-2$
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.