Question

How do you find the average value of `f(x)=x^5-2x^3-2` as x varies between `[-1,1]`?

Answer 1

Evaluate `1/(1-(-1)) int_-1^1 (x^5-2x^3-2) dx`

Explanation:

`1/(1-(-1)) int_-1^1 (x^5-2x^3-2) dx = 1/2 int_-1^1 (-2) dx`

(The first two terms form an odd function whose integral from `-1` to `1` is `0`.)

`= 1/2(-4) = -2`