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

1 Answer

Nov 22, 2016

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 $0$ .)

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

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