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: 21

Answer

\[ - \frac{7}{z} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{7}{{{z^2}}}dz} \hfill \\ Write\,\,\frac{1}{{{z^2}}}\,as\,\,{z^{ - 2}} \hfill \\ \int_{}^{} {7{z^{\,\, - 2}}dz} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{z^n}dz} = \frac{{{z^{n + 1}}}}{{n + 1}} + C \hfill \\ Then \hfill \\ \int_{}^{} {7{z^{ - 2}}dz} = 7\,\left( {\frac{{{z^{ - 2 + 1}}}}{{ - 2 + 1}}} \right) + C \hfill \\ Simplifying \hfill \\ 7\,\left( {\frac{{{z^{ - 1}}}}{{ - 1}}} \right) + C \hfill \\ - \frac{7}{z} + C \hfill \\ \end{gathered} \]
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