What is the average value of the function f(x) = x^2 on the interval [0,3]?

1 Answer
Mar 23, 2016

The average value is $3$.

Explanation:

The average value of a function $f$ on an interval $\left[a , b\right]$ is

$\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

So the value we seek is

$\frac{1}{3 - 0} {\int}_{0}^{3} {x}^{2} \mathrm{dx}$

 = 1/3 x^3/3]_0^3

$= {\left(3\right)}^{3} / 9 - {\left(0\right)}^{3} / 9 = 3$