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: 36

Answer

7

Work Step by Step

\[\begin{gathered} \int_0^{\ln 8} {{e^x}} dx \hfill \\ \hfill \\ {\text{using }}\int {{e^x}} dx = {e^x} + C \hfill \\ \hfill \\ \int_0^{\ln 8} {{e^x}} dx = \left[ {{e^x}} \right]_0^{\ln 8} \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ \left[ {{e^x}} \right]_0^{\ln 8} = {e^{\ln 8}} - {e^0} \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ 8 - 1 \hfill \\ \hfill \\ 7 \hfill \\ \end{gathered} \]
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