Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - Chapter 6 Review Exercises - Page 486: 80

$$A = 3$$

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