Answer
$1.1752$
Work Step by Step
We are given that $f(x)=e^{x}$, interval $[-1,1]$
Apply formula: $\overline{f}=\dfrac{1}{b-a}\int_a^b f(x) \ dx$
So, we have: $\overline{f}=\dfrac{1}{1-(-1)}\int_{-1}^2 e^{x} \ dx=\dfrac{1}{2}\int_{-1}^2 e^{x} \ dx$
or, $=\dfrac{1}{2}[e^{x}]_{-1}^1$
or, $=\dfrac{1}{2}(e^{1}-e^{-1})$
Thus, $ \overline{f}\approx 1.1752$
