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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 $\square$.

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Answer

Final Answer: $\boxed{-5}$

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 $\frac{1}{b-a}\int_{a}^{b}f(x)dx$.

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

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: $\boxed{-5}$