Explanation Given information: f avg a , b denote the average value of f on the interval a , b . Concept used: Consider the real valued function with independent variable of t under the interval of a , b as follows: f x The average value of the function f x under the interval a , b , is as follows: f avg = 1 b − a ∫ a b f x d x . Calculation: Split the expression of equation f avg = 1 b − a ∫ a b f x d x for the condition of a < c < b , it follows: f avg = 1 b − a ∫ a b f x d x = 1 b − a ∫ a c f x d x + ∫ c b f x d x = 1 b − a ∫ a c f x d x + 1 b − a ∫ c b f x d x Simplify it as follows

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ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Chapter 6.5, Problem 26E

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To show: favga,b=c−ab−afavga,c+b−cb−afavgc,b .

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Chapter 6.5, Problem 25E

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f avg a , b = c − a b − a f avg a , c + b − c b − a f avg c , b .

Solution Summary: The author analyzes the expression of the equation f_avgleft[a,bright].

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To show: favga,b=c−ab−afavga,c+b−cb−afavgc,b .

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