Explanation Given: The function f ( x ) = ln x , and the interval [ 1 , 5 ] . Concept Used: 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 . 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: In order to approximate the average value of f ( x ) = ln x on the interval [ 1 , 5 ] using a sample size of eight, observe that Δ x = b − a n = 5 − 1 8 = 4 8 = 1 2 So, the interval can be divided into subintervals as a = 1 , 3 2 , 2 , 5 2 ,

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.6, Problem 54S

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To approximate the average value of f(x)=lnx on the interval [1, 5] using a sample size of at least eight.

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Chapter 4.6, Problem 53S

Chapter 4.6, Problem 55S

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Chapter 4 Solutions

Calculus

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To approximate the average value of f ( x ) = ln x on the interval [ 1 , 5 ] using a sample size of at least eight.

Solution Summary: The author calculates the average value of an integrable function f on the interval left[1,5right] using a sample size of at least eight.

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To approximate the average value of f(x)=lnx on the interval [1, 5] using a sample size of at least eight.

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