Answer
$${f_{avg}} = \frac{{{e^{\ln 5}} - {e^{ - 1}}}}{{\ln 5 + 1}}$$
Work Step by Step
$$\eqalign{
& {\text{The average value of the function is:}} \cr
& {f_{avg}} = \frac{1}{{\ln 5 + 1}}\int_{ - 1}^{\ln 5} {{e^x}} dx \cr
& {\text{Integrate and evaluate}} \cr
& {f_{avg}} = \frac{1}{{\ln 5 + 1}}\left[ {{e^x}} \right]_{ - 1}^{\ln 5} \cr
& {f_{avg}} = \frac{1}{{\ln 5 + 1}}\left[ {{e^{\ln 5}} - {e^{ - 1}}} \right] \cr
& {f_{avg}} = \frac{{{e^{\ln 5}} - {e^{ - 1}}}}{{\ln 5 + 1}} \cr} $$
