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: 17

Answer

\[\frac{8}{3}{v^{3/2}} - \frac{6}{5}{v^{5/2}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {4\sqrt v - 3{v^{3/2}}} \right)dv} \hfill \\ Write\,\,\sqrt v \,\,as\,\,{v^{1/2}} \hfill \\ \int_{}^{} {\,\left( {4{v^{1/2}} - 3{v^{3/2}}} \right)dv} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{v^n}dx} = \frac{{{v^{n + 1}}}}{{n + 1}} + C \hfill \\ 4\,\left( {\frac{{{v^{3/2}}}}{{3/2}}} \right) - 3\,\left( {\frac{{{v^{5/2}}}}{{5/2}}} \right) + C \hfill \\ Simplifying \hfill \\ \frac{8}{3}{v^{3/2}} - \frac{6}{5}{v^{5/2}} + C \hfill \\ \end{gathered} \]
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