Question

What is the average value of the function `f(x) = 9 − x^2` on the interval `[-3,3]`?

Answer 1

It is `6`

Explanation:

The average value of a function `f(x)` on the interval `[a, b]` is

`f_(avg)=1/(b-a)*int_a^b f(x)dx`

Hence

#f_(avg)=1/(3-(-3))*int_-3^3 (9-x^2)dx=> f_(avg)=1/6*36=6#