Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.1 Antiderivatives - 7.1 Exercises: 29

Answer

\[ - 15{e^{ - 0.2x}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {3{e^{ - 0.2x}}dx} \hfill \\ \int_{}^{} {kg\,\left( x \right)dx = k\int_{}^{} {g\,\left( x \right)dx} } \hfill \\ 3\int_{}^{} {{e^{ - 0.2x}}dx} \hfill \\ Use\,\,integral\,of\,\,\exp onential\,\,functions \hfill \\ \int_{}^{} {{e^{kx}}dx} = \frac{{{e^{kx}}}}{k} + C \hfill \\ Then \hfill \\ 3\,\left( {\frac{{{e^{^{ - 0.2x}}}}}{{ - 0.2}}} \right) + C \hfill \\ Simplifying \hfill \\ 3\,\left( { - 5{e^{ - 0.2x}}} \right) + C \hfill \\ - 15{e^{ - 0.2x}} + C \hfill \\ \end{gathered} \]
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