# What is the average value of a function y = x <mrow class="MJX-TeXAtom-ORD"> 2

Ximena Skinner 2022-06-30 Answered
What is the average value of a function $y={x}^{2}-2x+4$ on the interval [0,8]?
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Explanation:
By definition
${y}_{ave}=\frac{{\int }_{a}^{b}ydx}{b-a}$
so here
${y}_{ave}=\frac{{\int }_{0}^{8}{x}^{2}-2x+4dx}{8-0}$
$=\frac{1}{8}\left[\frac{{x}^{3}}{3}-{x}^{2}+4x{\right]}_{0}^{8}$
$=\frac{52}{3}$

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