Explanation Given information: The provided equation is: f ( x ) = x 3 − x and the interval is [ − 1 , 1 ] Formula used: Average value The average value of a continuous function y = f ( x ) over the interval [ a , b ] is: Average value = 1 b − a ∫ a b f ( x ) d x Calculation: The provided function is: f ( x ) = x 3 − x And the interval is [ − 1 , 1 ] Consider the formula: Average value = 1 b − a ∫ a b f ( x ) d x Substitute − 1 for a and 1 for b and x 3 − x for f ( x ) in above equation to get: Average value = 1 1 − ( − 1 )

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Chapter 13.3, Problem 29E

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To calculate: The average value of the function f(x)=x3−x over the interval [−1,1].

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Chapter 13.3, Problem 28E

Chapter 13.3, Problem 30E

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Chapter 13 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The average value of the function f ( x ) = x 3 − x over the interval [ − 1 , 1 ] .

Solution Summary: The author calculates the average value of a continuous function y=f(x) over the interval

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To calculate: The average value of the function f(x)=x3−x over the interval [−1,1].

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Chapter 13 Solutions