Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - Review Exercises: 17

Answer

\[ = 20\]

Work Step by Step

\[\begin{gathered} \int_0^2 {\,{{\left( {x + 1} \right)}^3}dx} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \,\,\left[ {\frac{{\,{{\left( {x + 1} \right)}^4}}}{4}} \right]_0^2 \hfill \\ \hfill \\ Fundamental\,\,theorem \hfill \\ \hfill \\ = \frac{{\,{{\left( {2 + 1} \right)}^4}}}{4} - \frac{{\,{{\left( {0 + 1} \right)}^4}}}{4} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{{81}}{4} - \frac{1}{4} = \frac{{80}}{4} \hfill \\ \hfill \\ = 20 \hfill \\ \end{gathered} \]
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