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: 20

Answer

\[16{t^{7/2}} + 4{t^{9/2}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{\,^{}}\left( {56{t^{5/2}} + 18{t^{7/2}}} \right)dt} \hfill \\ Use\,\,the\,\,sum\,\,and\,\,difference\,\,rules \hfill \\ \int_{}^{} {56{t^{5/2}}dt + \int_{}^{} {18{t^{7/2}}dt} } \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ 56\,\left( {\frac{{{t^{5/2 + 1}}}}{{5/2 + 1}}} \right) + 18\,\left( {\frac{{{t^{7/2 + 1}}}}{{7/2 + 1}}} \right) + C \hfill \\ 56\,\left( {\frac{{{t^{7/2}}}}{{7/2}}} \right) + 18\,\left( {\frac{{{t^{9/2}}}}{{9/2}}} \right) + C \hfill \\ Simplifying \hfill \\ 16{t^{7/2}} + 4{t^{9/2}} + C \hfill \\ \end{gathered} \]
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