Explanation Given: The function f ( x ) = 4 x 3 / 2 , and the interval [ 0 , 2 ] . 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 ) = 4 x 3 / 2 on the interval [ 0 , 2 ] is given by, f avg = 1 2 − 0 ∫ 0 2 ( 4 x 3 / 2 ) d x <

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.6, Problem 62S

To determine

The exact average value of f(x)=4x3/2 on the interval [0, 2] using definite integrals and the Fundamental Theorem of Calculus.

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Chapter 4.6, Problem 61S

Chapter 4.6, Problem 63S

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Chapter 4 Solutions

Calculus

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The exact average value of f ( x ) = 4 x 3 / 2 on the interval [ 0 , 2 ] 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)=4x3/2 on the interval [0, 2] using definite integrals and the Fundamental Theorem of Calculus.

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