Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - Review Exercises: 18

Answer

\[ = \frac{{199}}{{187}}\]

Work Step by Step

\[\begin{gathered} \int_0^1 {\,\left( {4{x^{21}} - 2{x^{16}} + 1} \right)\,dx} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ \,\,\left[ {\frac{{2{x^{22}}}}{{11}} - \frac{{2{x^{17}}}}{{17}} + x} \right]_0^1 \hfill \\ \hfill \\ Fundamental\,\,theorem \hfill \\ \hfill \\ = \frac{{2\,{{\left( 1 \right)}^{22}}}}{{11}} - \frac{{2\,{{\left( 1 \right)}^{17}}}}{{17}} + 1 - 0 \hfill \\ \hfill \\ = \frac{2}{{11}} - \frac{2}{{17}} + 1 \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{{199}}{{187}} \hfill \\ \end{gathered} \]
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