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What is the average value of the function $f(x) = x - (x^2)$ on the interval $[0,2]$ ?

1 Answer

Sep 21, 2016

The average value of $f$ on $[a,b}$ is $1/(b-a) int_a^b f(x) dx$ .

Explanation:

For this function on this interval, I get $-1/3$

Ave $= 1/(2-0) int_0^2 (x-x^2) dx$

$= 1/2[x^2/2-x^3/3]_0^2$

$= 1/2[(4/2-8/3)-(0)]$

$= 1/2(-2/3) = -1/3$

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