Calculus: Early Transcendentals 8th Edition

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

Chapter 5 - Review - Exercises - Page 423: 55

Answer

$\int_{0}^{1}e^x~cos~x~dx \leq e-1$

Work Step by Step

Note that $e^x \gt 0$ for all $x$ On the interval $[0,1]$: $cos~x \leq 1$ $e^x~cos~x \leq e^x$ Therefore: $\int_{0}^{1}e^x~cos~x~dx \leq \int_{0}^{1}e^x~dx$ $\int_{0}^{1}e^x~cos~x~dx \leq e^x~\Big\vert_{0}^{1}$ $\int_{0}^{1}e^x~cos~x~dx \leq e-1$
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