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: 15

Answer

\[\frac{5}{4}{x^4} - 20{x^2} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {5x\,\left( {{x^2} - 8} \right)dx} \hfill \\ Simplifying\,\,the\,\,in\,tegrand\,\,and\,\,then \hfill \\ find\,\,the\,\,antiderivative \hfill \\ \int_{}^{} {\,\left( {5{x^3} - 40x} \right)dx} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ 5\,\left( {\frac{{{x^4}}}{4}} \right) - 40\,\left( {\frac{{{x^2}}}{2}} \right) + C \hfill \\ Simplifying \hfill \\ \frac{5}{4}{x^4} - 20{x^2} + C \hfill \\ \end{gathered} \]
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