Explanation Given: The function f ( x ) = 1 3 x + 1 , and the interval [ 2 , 5 ] . Concept Used: The average value of an integrable functionf on the interval [ a , b ] , is given by 1 b − a ∫ a b f ( x ) d x . The area that is bounded by the graph of f ( x ) above the x-axis is positive. The area that is bounded by the graph of f ( x ) below the x-axis is negative. Power rule of integration: ∫ x n d x = x n + 1 n + 1 Calculation: Observe that the average value of an integrable function f on the interval [ a , b ] , is given by 1 b − a ∫ a b f ( x ) d x , so using this concept the exact average value of f ( x ) = 1 3 x + 1 on the interval [ 2 , 5 ] is given by, f avg = 1 5 − 2 ∫ 2 5

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 4.6, Problem 64S

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The exact average value of f(x)=13x+1 on the interval [2, 5] using definite integrals and the Fundamental Theorem of Calculus.

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Chapter 4.6, Problem 63S

Chapter 4.6, Problem 65S

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The exact average value of f ( x ) = 1 3 x + 1 on the interval [ 2 , 5 ] using definite integrals and the Fundamental Theorem of Calculus.

Solution Summary: The author calculates the average value of an integrable function f on the interval left[a,bright] using definite integrals and the Fundamental Theorem of Calculus.

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The exact average value of f(x)=13x+1 on the interval [2, 5] using definite integrals and the Fundamental Theorem of Calculus.

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