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

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

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*}