Explanation Given: The function f ( x ) = 100 ( 1 − x ) , and the interval [ a , b ] = [ 0 , 10 ] . 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: In order to find the real number c ∈ ( a , b ) such that f ( c ) is the average value of f on the interval [ a , b ] , first find the average value of the function on the given interval and set it equal to f ( c ) and solve for c. 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 ) = 100 ( 1 − x ) on the interval [ 0 , 10 ] is given by, f avg = 1 10 − 0 ∫ 0 10 ( 100 ( 1 − x ) )

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 4.6, Problem 72S

To determine

A real number c∈(a,b) such that

f(c) is the average value of f(x)=100(1−x) on the interval [a, b]=[0, 10] .

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Chapter 4.6, Problem 71S

Chapter 4.6, Problem 73S

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A real number c ∈ ( a , b ) such that f ( c ) is the average value of f ( x ) = 100 ( 1 − x ) on the interval [ a , b ] = [ 0 , 10 ] .

Solution Summary: The author calculates the average value of an integrable function f on the interval left[a,bright].

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A real number c∈(a,b) such that

f(c) is the average value of f(x)=100(1−x) on the interval [a, b]=[0, 10] .

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Chapter 4 Solutions

A real number c ∈ ( a , b ) such that f ( c ) is the average value of f ( x ) = 100 ( 1 − x ) on the interval [ a , b ] = [ 0 , 10 ] .

Solution Summary: The author calculates the average value of an integrable function f on the interval left[a,bright].

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A real number c∈(a,b) such that f(c) is the average value of f(x)=100(1−x) on the interval [a, b]=[0, 10] .

Want to see the full answer?

Chapter 4 Solutions

A real number c∈(a,b) such that

f(c) is the average value of f(x)=100(1−x) on the interval [a, b]=[0, 10] .