Explanation Given: The given function is f ( x ) = 9 − x 2 and the given interval is [ − 3 , 3 ] . Concept used: Average value of a function on a closed interval: If a function f is continuous on the interval [ a , b ] , then the average value of f is given by A .V = 1 ( b − a ) ∫ a b f ( x ) d x Formula used: Area of a semi-circle with radius r unit is given by A = π 2 r 2 Calculation: Consider the given function and the interval. f ( x ) = 9 − x 2 and [ − 3 , 3 ] Here, a = − 3 , b = 3 Now, calculate the value of the integral ∫ − 3 3 9 − x 2 d x as follows: The region bounded by f and the x -axis on [ − 3 , 3 ] is shown below. The function f ( x ) = 9 − x 2 is continuous on [ − 3 , 3 ]

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 5.7, Problem 41PS

To determine

To find: The average value of the given function on the interval [−3,3] .

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Chapter 5.7, Problem 40PS

Chapter 5.7, Problem 42PS

Chapter 5 Solutions

Calculus

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The average value of the given function on the interval [ − 3 , 3 ] .

Solution Summary: The author calculates the average value of a function on the interval left[-3,3right].

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To find: The average value of the given function on the interval [−3,3] .

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Chapter 5 Solutions