Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - Review Exercises: 16

Answer

\[ = \frac{1}{3}\sin \,\left( {3x} \right) + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\cos \,3xdx} \hfill \\ \hfill \\ set\,\,u = 3x\,\,\,\,\,then\,\,\,\,du = 3dx \hfill \\ and\,\,\,dx = \frac{{du}}{3} \hfill \\ \hfill \\ apply\,\,the\,\,\,substitution \hfill \\ \hfill \\ \int_{}^{} {\cos \,u\,\left( {\frac{{du}}{3}} \right) = \frac{1}{3}\int_{}^{} {\cos udu} } \hfill \\ \hfill \\ integrate\,\,\,use\,\,\,\int_{}^{} {\cos udu = \sin u + C} \hfill \\ \hfill \\ = \frac{1}{3}\sin u + C \hfill \\ \hfill \\ {\text{Replace }}u{\text{ with }}3x \hfill \\ \hfill \\ = \frac{1}{3}\sin \,\left( {3x} \right) + C \hfill \\ \hfill \\ \end{gathered} \]
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