Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.4 Graphs And Applications Involving Logarithmic And Exponential Functions - Exercises Set 6.4 - Page 440: 44

$$A = 1$$

$$\eqalign{ & {\text{From the graph we can note that the area is given by:}} \cr & A = \int_1^e {\frac{1}{y}} dy \cr & {\text{Integrating}} \cr & A = \left[ {\ln \left| y \right|} \right]_1^e \cr & {\text{Simplifying}} \cr & A = \ln e - \ln 1 \cr & A = 1 \cr} $$