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: 14

Answer

\[\frac{4}{5}{t^{5/4}} + {\pi ^{1/4}}t + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {{t^{1/4}} + {\pi ^{1/4}}} \right)dt} \hfill \\ Extending\,\,using\,\,the\,\,sum\,\,and \hfill \\ difference\,\,rules \hfill \\ \int_{}^{} {{t^{1/4}}dt + {\pi ^{1/4}}} \int_{}^{} {dt} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{t^n}dt} = \frac{{{t^{n + 1}}}}{{n + 1}} + C \hfill \\ \frac{{{t^{1/4 + 1}}}}{{1/4 + 1}} + {\pi ^{1/4}}t + C \hfill \\ Simplifying \hfill \\ \frac{4}{5}{t^{5/4}} + {\pi ^{1/4}}t + C \hfill \\ \end{gathered} \]
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