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

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

1 Answer

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Answer 1 · 2016-11-22T13:29:26

Evaluate $\frac{1}{1 - (- 1)} \int_{- 1}^{1} (x^{5} - 2 x^{3} - 2) d x$ $1/(1-(-1)) int_-1^1 (x^5-2x^3-2) dx$

Explanation:

$\frac{1}{1 - (- 1)} \int_{- 1}^{1} (x^{5} - 2 x^{3} - 2) d x = \frac{1}{2} \int_{- 1}^{1} (- 2) d x$ $1/(1-(-1)) int_-1^1 (x^5-2x^3-2) dx = 1/2 int_-1^1 (-2) dx$

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

$= \frac{1}{2} (- 4) = - 2$ $= 1/2(-4) = -2$

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

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