Answer
$\dfrac{5}{4} $ or, $\approx 1.25$
Work Step by Step
We are given that $f(x)=|-x+2|$, interval $[-1,3]$
Apply formula: $\overline{f}=\dfrac{1}{b-a}\int_a^b f(x) \ dx$
So, we have: $\overline{f}=\dfrac{1}{3-(-1)}\int_{-1}^3 |-x+2| \ dx=\dfrac{1}{4} \int_{-1}^3 |-x+2| \ dx$
Apply formula: $\int |px+q| \ dx=\dfrac{1}{2p} (px+q)|px+q|+C$
So, we can write as: $\overline{f}=\dfrac{1}{4}[\dfrac{1}{(2)(-1)}(-x+2)|-x+2|]_{-1}^3$
or, $=\dfrac{-1}{8}[(-x+2)|-x+2|]_{-1}^3$
or, $=\dfrac{-1}{8}(-1)+\dfrac{1}{8}(9)$
Thus, $ \overline{f}=\dfrac{5}{4} \approx 1.25$
