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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the average value of the function f on the given interval. f(x) = x, [0, 16].
Solution:
Given: Function f(x) = x and the interval [0, 16]
The average of a function can be defined by the mean value theorem.
The mean value theorem states that y = (x) be a continuous function on the closed interval [a,b].
The mean value theorem for integrals states that there exists a point c in that interval such that
f(c) = 1/(b - a) \(\int_{a}^{b} f(x)dx\)
Here the lower limit is 0 and the upper limit is 16.
i.e., a = 0 and b = 16
f(c) = 1/(16 - 0) \(\int_{0}^{16} f(x)dx\)
f(c) = 1/16 \(\frac{x^2}{2}]^{16}_{0}\)
f(c) = 1/16(162/2 - 02)
f(c) = 16/2 = 8
f(c) = 8
The average value of f(x) is 8
Find the average value of the function f on the given interval. f(x) = x, [0, 16].
Summary:
The average value of the function f on the given interval. f(x) = x, [0, 16] is 8.
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