Answer
$$\overline f = \frac{1}{{e - 1}}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{1}{x}{\text{ on the interval }}\left[ {1,e} \right] \cr
& {\text{Find the average value using }}\overline f = \frac{1}{{b - a}}\int_a^b {f\left( x \right)} dx \cr
& \overline f = \frac{1}{{e - 1}}\int_1^e {\frac{1}{x}} dx \cr
& {\text{Integrate}} \cr
& \overline f = \frac{1}{{e - 1}}\left[ {\ln x} \right]_1^e \cr
& \overline f = \frac{1}{{e - 1}}\left( {\ln e - \ln 1} \right) \cr
& \overline f = \frac{1}{{e - 1}} \cr
& \cr
& {\text{Graph}} \cr} $$
