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

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ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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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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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 TRANS.-SAPLINGPLUS

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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

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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]