Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 87


$\frac{e^{2}}{2} -e +\frac{1}{2}.$

Work Step by Step

The area between the two curves can be calculated as follows: \begin{align*} Area\ &=\int_0^1e^{2x}-e^xdx \\ &=(\frac{1}{2} e^{2x}-e^x)_0^1\\ &=\frac{e^{2}}{2} -e -(\frac{1}{2}-1)\\ &=\frac{e^{2}}{2} -e +\frac{1}{2}. \end{align*}
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