Find the average value fave of the function f on the given interval.
f(x) = 

x
,    [0, 4]

To find the average value of a function \( f(x) \) on an interval \([a, b]\), you use the formula:

\[
f_{\text{ave}} = \frac{1}{b - a} \int_a^b f(x) \, dx
\]

In this case, \( f(x) = x \) and the interval is \([0, 4]\). So, we plug these values into the formula:

\[
f_{\text{ave}} = \frac{1}{4 - 0} \int_0^4 x \, dx = \frac{1}{4} \int_0^4 x \, dx
\]

Now, we compute the integral:

\[
\int_0^4 x \, dx = \left[\frac{x^2}{2}\right]_0^4 = \frac{4^2}{2} - \frac{0^2}{2} = \frac{16

Find the average value fave of the function f on the given interval. f(x) = x, [0, 4]

Learn how to find the average value of the function f(x) = x over the interval [0, 4]. This problem covers key calculus concepts, including definite integration and the fundamental theorem of calculus, suitable for students in Grades 11-12 or early college.

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