Explanation Given: A function f ( x , y ) = e x y The equation of the ellipse x 2 2 + y 2 = 1 Calculation: The average value of f ( x , y ) = e x y is f ¯ = 1 Area of given region ∫ ∫ R f ( x , y ) d A The area of the ellipse is π 2 Therefore, f ¯ = 1 Area of given region ∫ ∫ R

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 40CRE

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The average value of $f (x, y) = e^{x y}$

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Chapter 16, Problem 39CRE

Chapter 16, Problem 41CRE

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The average value of f ( x , y ) = e x y

Solution Summary: The author calculates the average value of the function f (x, y) = e x.

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To calculate: The average value of f(x,y)=exy

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Chapter 16 Solutions

To calculate:

The average value of $f (x, y) = e^{x y}$