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Find the average value of \frac{3}{x^{3}} on the closed interval [1,4]. (a) \frac{45}{32} (b)...

Question:

Find the average value of {eq}\frac{3}{x^{3}} {/eq} on the closed interval {eq}[1,4] {/eq}. (a) {eq}\frac{45}{32} {/eq} (b) {eq}\frac{15}{32} ( {/eq}c) {eq}\frac{15}{16} {/eq} (d) {eq}\frac{5}{16} {/eq} (e) {eq}\frac{45}{16} {/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 function {eq}\displaystyle f(x) = \frac{3}{x^3} {/eq}

Average value of a function on closed interval {eq}\displaystyle [1,4] {/eq} is given...

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Law of Averages: Definition & Formula

from General Studies Math: Help & Review

Chapter 5 / Lesson 8
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