Find the average function value over the given interval (a) y = 4 - x^2; [-2, 2]. (b) f (x) = x^2...

Question:

Find the average function value over the given interval

(a) {eq}\displaystyle y = 4 - x^2\ ; [-2,\ 2] {/eq}.

(b) {eq}\displaystyle f (x) = x^2 + x - 2\ ; [0,\ 4] {/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:

(a) Given {eq}\displaystyle y =4-x^2 {/eq}

Average value of function on interval {eq}\displaystyle [-2,2] {/eq} is

{eq}\displaystyle...

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Law of Averages: Definition & Formula

from General Studies Math: Help & Review

Chapter 5 / Lesson 8
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