Explanation Given information: The function f ( x ) have a revolution about the x-axis for the given function and interval: f ( x ) = n sin n x [ 0 , π n ] Concept used: The average value of an integrable function f on [ a , b ] is the given by: A v e r a g e v a l u e = 1 b − a ∫ a b f ( x ) d x Substitution method of integration : This formula is used to transform one integral into another integral and that integral will be easy to calculate. Integration of ∫ a b sin x d x = − cos x Calculation: Here, the function f ( x ) = x n with the interval [ a , b ] . So, a = 0 , b = π n A v e r a g e v a l u e = 1 b − a ∫ a b f ( x ) d x = 1 0 − π n ∫ 0 π n n sin n x d x

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 6.2, Problem 47E

To determine

Calculate the average value f(x) over the given interval:

f(x)=nsinnx [0,πn]

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Chapter 6.2, Problem 46E

Chapter 6.2, Problem 48E

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Chapter 6 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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Calculate the average value f ( x ) over the given interval: f ( x ) = n sin n x [ 0 , π n ]

Solution Summary: The author calculates the average value of an integrable function f(x) over the given interval.

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Calculate the average value f(x) over the given interval:

f(x)=nsinnx [0,πn]

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Chapter 6 Solutions

Calculate the average value f ( x ) over the given interval: f ( x ) = n sin n x [ 0 , π n ]

Solution Summary: The author calculates the average value of an integrable function f(x) over the given interval.

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Calculate the average value f(x) over the given interval: f(x)=nsinnx [0,πn]

Want to see the full answer?

Chapter 6 Solutions

Calculate the average value f(x) over the given interval:

f(x)=nsinnx [0,πn]