Explanation Given information: The given function is f ( x ) = x n and the interval is [ 0 , a ] . 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 . Integration of ∫ x n + 1 = 1 n + 1 x n + 1 + C . Calculation: Here, the function f ( x ) = x n with the interval [ a , b ] . So, a = 0 , b = a Average value = 1 b − a ∫ a b f ( x ) d x = 1 a − 0 ∫ 0 a x n d x = 1 a ∫ 0 a

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ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Question

Chapter 6.2, Problem 49E

To determine

The average over the given interval [0,a] of the function f(x)=xn.

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Chapter 6.2, Problem 48E

Chapter 6.2, Problem 50E

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Chapter 6 Solutions

EBK 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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The average over the given interval [ 0 , a ] of the function f ( x ) = x n .

Solution Summary: The author calculates the average over the given interval [0,a] of the function f(x)=xn.

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The average over the given interval [0,a] of the function f(x)=xn.

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Chapter 6 Solutions