cooloicons62

2022-06-29

How do you find the average value of ${x}^{3}$ as x varies between -1 and 2

Oliver Shepherd

Expert

Average value of f(x) over interval [a,b] is $f\left(x\right)=\frac{{\int }_{a}^{b}f\left(x\right)dx}{b-a}$
Here that means that:
$f\left(x\right)=\frac{{\int }_{-1}^{2}{x}^{3}dx}{2-\left(-1\right)}$
$=\frac{\left[\frac{{x}^{4}}{4}{\right]}_{-1}^{2}}{3}=\frac{5}{4}$

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