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

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Answer 1 · 2016-04-19T14:01:12

The average value of $f$ $f$ on interval $[a, b]$ $[a,b]$ is $\frac{1}{b - a} \int_{a}^{b} f (x) d x$ $1/(b-a) int_a^b f(x) dx$

So the average value of $f (x) = 3 x^{2} - 2$ $f(x) = 3x^2-2$ on the interval $[(0, 2]$ $[(0,2]$ is

$\frac{1}{2 - 0} \int_{0}^{2} (3 x^{2} - 2) d x$ $1/(2-0) int_0^2 (3x^2-2) dx$ , $" "$ which is $2$ $2$ .

What is the average value of a function f(x)=3x2−2f(x)=3x^2 - 2 on the interval [0,2][0,2]?