annie1799
annie1799 annie1799
  • 20-04-2021
  • Mathematics
contestada

Find the average of f(x)=x^3-x over [0,2]

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sqdancefan
sqdancefan sqdancefan
  • 21-04-2021

9514 1404 393

Answer:

  1

Step-by-step explanation:

The average value of the function is the integral over the interval, divided by the width of the interval.

  [tex]\displaystyle\overline{y}=\frac{1}{2-0}\int_0^2{f(x)}\,dx=\left.\frac{1}{2}\left(\frac{x^4}{4}-\frac{x^2}{2}\right)\right|_0^2=\frac{1}{2}\left(\frac{2^4}{4}-\frac{2^2}{2}\right)=\frac{4-2}{2}\\\\\boxed{\overline{y}=1}[/tex]

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