Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 355: 125

$$A = {e^5} - 1$$

$$\eqalign{ & {\text{From the graph we can see that the region is given by:}} \cr & A = \int_0^5 {{e^x}} dx \cr & {\text{Integrate and evaluate}} \cr & A = \left[ {{e^x}} \right]_0^5 \cr & A = {e^5} - {e^0} \cr & A = {e^5} - 1 \cr & A \approx 147.413 \cr} $$