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Find the average value of the function $f (x) = x^{2} - 17$ on $[0, 6]$ .

The average value of the function $f (x) = x^{2} - 17$ on $[0, 6]$ is $◻$ .

Answer

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Answer

Final Answer: $- 5$

Steps

Step 1 ：Let's find the average value of the function $f (x) = x^{2} - 17$ on the interval $[0, 6]$ .

Step 2 ：The average value of a function $f (x)$ on the interval $[a, b]$ is given by the formula $\frac{1}{b - a} \int_{a}^{b} f (x) d x$ .

Step 3 ：Substituting $f (x) = x^{2} - 17$ , $a = 0$ , and $b = 6$ into the formula, we get $\frac{1}{6 - 0} \int_{0}^{6} (x^{2} - 17) d x$ .

Step 4 ：Evaluating the integral, we find that the average value of the function $f (x) = x^{2} - 17$ on $[0, 6]$ is -5.

Step 5 ：Final Answer: $- 5$