Explanation Formula used: The average value of the function f on the interval [ a , b ] is 1 b − a ∫ a b f ( x ) d x . Calculation: The function is f ( x ) = 2 − 3 x 2 over the interval [ 1 , 3 ] . Here, a = 1 and b = 3 . Substitute the respective values and find the average value of the function as follows. Average value = 1 3 − 1 ∫ 1 3 ( 2 − 3 x 2 ) d x = 1 2 [ 2 x − 3 x 2 + 1 2 + 1 ] 1 3

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 16.2, Problem 24E

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To find: The average value of the function f(x)=2−3x2 on the interval [1,3] .

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Chapter 16.2, Problem 23E

Chapter 16.2, Problem 25E

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Chapter 16 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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The average value of the function f ( x ) = 2 − 3 x 2 on the interval [ 1 , 3 ] .

Solution Summary: The author explains the formula used to find the average value of the function f on the interval left[1,3right].

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To find: The average value of the function f(x)=2−3x2 on the interval [1,3] .

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Chapter 16 Solutions