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Find the average value of the function f (x) = 3 square root x on the interval [1, 8].

Question:

Find the average value of the function {eq}\displaystyle f (x) = 3 \sqrt x {/eq} on the interval {eq}[1,\ 8] {/eq}.

Average value

Consider a function {eq}\displaystyle f(x) {/eq} .Then average value of the function {eq}\displaystyle f(x) {/eq} on the interval {eq}\displaystyle [a,b] {/eq} is given by

Average value {eq}\displaystyle = \frac{\int_a^bf(x)dx}{b-a} {/eq}

Answer and Explanation:

Given {eq}\displaystyle f(x)=3\sqrt{x} {/eq}

Average value of a function is given by {eq}\displaystyle \frac{\int_1^8 3\sqrt{x}dx}{8-1} {/eq}

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Law of Averages: Definition & Formula

from General Studies Math: Help & Review

Chapter 5 / Lesson 8
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