Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - Review Exercises: 15

Answer

\[\frac{{212}}{5}\]

Work Step by Step

\[\begin{gathered} \int_{ - 2}^2 {\,\left( {3{x^4} - 2x + 1} \right)dx} \hfill \\ \hfill \\ integrate\,\,\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C} \hfill \\ \hfill \\ \,\,\left[ {\frac{{3{x^5}}}{5} - {x^2} + x} \right]_{ - 2}^2 \hfill \\ \hfill \\ apply\,\,Fundamental\,\,theorem\,\,of\,\,calculus\,\,,\,therefore \hfill \\ \hfill \\ \,\,\left[ {\frac{{3\,{{\left( 2 \right)}^5}}}{5} - \,{{\left( 2 \right)}^2} + 2} \right] - \,\,\left[ {\frac{{3\,{{\left( { - 2} \right)}^5}}}{5} - \,\,\,{{\left( { - 2} \right)}^2} + 2} \right] \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ \left[ {\frac{{86}}{5}} \right] - \,\,\left[ { - \frac{{126}}{5}} \right] \hfill \\ \hfill \\ \frac{{212}}{5} \hfill \\ \end{gathered} \]
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