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: 19

Answer

\[4{u^{5/2}} - 4{u^{7/2}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {10{u^{3/2}} - 14{u^{5/2}}} \right)du} \hfill \\ using\,\,the\,\,sum\,\,and\,difference\,\,rules \hfill \\ \int_{}^{} {10{u^{3/2}}du - \int_{}^{} {14{u^{5/2}}du} } \hfill \\ Find\,\,the\,\,antiderivative\,\,\,use\,\,the\,\, \hfill \\ power\,\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ Then \hfill \\ 10\,\left( {\frac{{{u^{3/2 + 1}}}}{{3/2 + 1}}} \right) - 14\,\left( {\frac{{{u^{5/2 + 1}}}}{{5/2 + 1}}} \right) + C \hfill \\ 10\,\left( {\frac{{{u^{5/2}}}}{{5/2}}} \right) - 14\,\left( {\frac{{{u^{7/2}}}}{{7/2}}} \right) + C \hfill \\ Simplifying \hfill \\ 4{u^{5/2}} - 4{u^{7/2}} + C \hfill \\ \hfill \\ \end{gathered} \]
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