Explanation Given information: The function f ( x ) with the interval: f ( x ) = cosh n x for n ≠ 0 , [-1,1] 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 cosh x d x = sinh x Hyperbolic of sinh x = e x − e − x 2 Calculation: Here, the function f ( x ) = cosh n x for n ≠ 0 , [-1,1] . So, a = 1 , b = − 1 A v e r a g e v a l u e = 1 b − a ∫ a b f ( x ) d x = 1 − 1 − 1 ∫ 1 − 1 cosh n x (1) Here, we substitute the value: Assume: n x = u Differentiate with respect to x n d d x ( x ) = d d x u n d x = d u d x = d u n Put the value of

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Question

Chapter 6.2, Problem 48E

To determine

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

f(x)=coshnx for n≠0, [-1,1]

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Chapter 6.2, Problem 47E

Chapter 6.2, Problem 49E

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Chapter 6 Solutions

Calculus: Early Transcendentals

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Calculate the average value f ( x ) over the given interval: f ( x ) = cosh n x for n ≠ 0 , [-1,1]

Solution Summary: The author calculates the average value of f(x) over the given interval. Substitution method of integration is used to transform one integral into another integral.

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

f(x)=coshnx for n≠0, [-1,1]

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Chapter 6 Solutions

Calculate the average value f ( x ) over the given interval: f ( x ) = cosh n x for n ≠ 0 , [-1,1]

Solution Summary: The author calculates the average value of f(x) over the given interval. Substitution method of integration is used to transform one integral into another integral.

Concept explainers

Videos

Calculate the average value f(x) over the given interval: f(x)=coshnx for n≠0, [-1,1]

Want to see the full answer?

Chapter 6 Solutions

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

f(x)=coshnx for n≠0, [-1,1]