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: 13

Answer

\[\frac{{10}}{3}{z^{3/2}} + \sqrt 2 z + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {5\sqrt z + \sqrt 2 } \right)dz} \hfill \\ write\,\,\sqrt z \,\,as\,\,{z^{1/2}} \hfill \\ \int_{}^{} {\,\left( {5{z^{1/2}} + \sqrt 2 } \right)} dz \hfill \\ Extending\,\,using\,\,the\,\,sum\,\,and \hfill \\ difference\,\,rules \hfill \\ \int_{}^{} {5{z^{1/2}}\,dz} \int_{}^{} {\sqrt 2 dz} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ 5\,\left( {\frac{{{z^{3/2}}}}{{3/2}}} \right) + \sqrt 2 z + C \hfill \\ Simplifying \hfill \\ \frac{{10}}{3}{z^{3/2}} + \sqrt 2 z + C \hfill \\ \end{gathered} \]
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