Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.4 Graphs And Applications Involving Logarithmic And Exponential Functions - Exercises Set 6.4 - Page 440: 42

$$A = \ln 5$$

$$\eqalign{ & {\text{Let }}f\left( x \right) = \frac{1}{x};{\text{ }}\left[ {1,5} \right] \cr & {\text{The area is given by}} \cr & A = \int_1^5 {\frac{1}{x}} dx \cr & {\text{Integrating}} \cr & A = \left[ {\ln \left| x \right|} \right]_1^5 \cr & A = \ln 5 - \ln 1 \cr & {\text{Simplifying}} \cr & A = \ln 5 \cr} $$