Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 363: 84

Answer

$$A = \frac{8}{{3\ln 3}}$$

Work Step by Step

$$\eqalign{ & y = {3^{\cos x}}\sin x,{\text{ }}y = 0,{\text{ }}x = 0,{\text{ }}x = \pi \cr & {\text{From the graph, we can define the area enclosed by}} \cr & A = \int_0^\pi {{3^{\cos x}}\sin x} dx \cr & {\text{Integrating}} \cr & A = - \frac{1}{{\ln 3}}\left[ {{3^{\cos x}}} \right]_0^\pi \cr & A = - \frac{1}{{\ln 3}}\left[ {{3^{\cos \pi }} - {3^{\cos 0}}} \right] \cr & A = - \frac{1}{{\ln 3}}\left[ {{3^{ - 1}} - 3} \right] \cr & A = \frac{8}{{3\ln 3}} \approx 2.427 \cr} $$
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