Find the average value over the given interval.
$f (x) = x^{2} + x - 8; [0, 16]$
The average value of $f (x) = x^{2} + x - 8$ on $[0, 16]$ is (Type an integer or a simplified fraction.)

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Answer

The average value of $f (x) = x^{2} + x - 8$ on $[0, 16]$ is $\frac{256}{3}$ .

Steps

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

Step 2 ：In this case, $f (x) = x^{2} + x - 8$ , $a = 0$ , and $b = 16$ . So we need to calculate the integral of $f (x)$ from $0$ to $16$ , and then divide by $16 - 0 = 16$ .

Step 3 ：Calculate the integral of $f (x)$ from $0$ to $16$ .

Step 4 ：Divide the result by $16$ to get the average value.

Step 5 ：The average value of $f (x) = x^{2} + x - 8$ on $[0, 16]$ is $\frac{256}{3}$ .

Find the average value over the given interval.f(x)=x2+x−8;[0,16]The average value of f(x)=x2+x−8 on [0,16] is (Type an integer or a simplified fraction.)

Answer

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Find the average value over the given interval.
$f (x) = x^{2} + x - 8; [0, 16]$
The average value of $f (x) = x^{2} + x - 8$ on $[0, 16]$ is (Type an integer or a simplified fraction.)