The average value of a function, f(x), over the interval [a, b] is given by the formula:

fave = (1/(b-a)) * ∫ from a to b of f(x) dx

Here, our function f(x) = x and the interval is [0, 16]. So, a = 0 and b = 16.

Let's calculate the integral first:

∫ from 0 to 16 of x dx = [0.5*x^2] from 0 to 16 = 0.5*16^2 - 0.5*0^2 = 128.

Now, we can find the average value:

fave = (1/(16-0)) * 128 = 8.

So, the average value of the function f(x) = x on the interval [0, 16] is 8.

Question

The average value of a function, f(x), over the interval [a, b] is given by the formula:

fave = (1/(b-a)) * ∫ from a to b of f(x) dx

Here, our function f(x) = x and the interval is [0, 16]. So, a = 0 and b = 16.

Let's calculate the integral first:

∫ from 0 to 16 of x dx = [0.5*x^2] from 0 to 16 = 0.5*16^2 - 0.5*0^2 = 128.

Now, we can find the average value:

fave = (1/(16-0)) * 128 = 8.

So, the average value of the function f(x) = x on the interval [0, 16] is 8.

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