Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - Chapter 6 Review Exercises - Page 486: 79

$$A = {e^3} - e$$

$$\eqalign{ & f\left( x \right) = {e^x};{\text{ }}\left[ {1,3} \right] \cr & {\text{The area is given by}} \cr & A = \int_1^3 {{e^x}dx} \cr & {\text{Integrating}} \cr & A = \left[ {{e^x}} \right]_1^3 \cr & A = {e^3} - {e^1} \cr & A = {e^3} - e \cr} $$