Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 48

Answer

\[5\left( {{e^2} - 1} \right)\]

Work Step by Step

\[\begin{gathered} \int_0^1 {10{e^{2x}}} dx \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ 10\int_0^1 {{e^{2x}}} dx \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ 10\left( {\frac{1}{2}} \right)\left[ {{e^{2x}}} \right]_0^1 \hfill \\ \hfill \\ 5\left[ {{e^{2x}}} \right]_0^1 \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ 5\left[ {{e^{2\left( 1 \right)}} - {e^{2\left( 0 \right)}}} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ 5\left( {{e^2} - 1} \right) \hfill \\ \end{gathered} \]
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