Explanation Approach: Average value of function f ( x , y ) over a region R is f A v g = 1 A ∬ R f ( x , y ) d x d y where A is the area covered by region R . Calculation: Given: function f ( x , y ) = e − 5 y + 3 x and region 0 ≤ x ≤ 2 , 0 ≤ y ≤ 2 Area covered by region A = 2 × 2 = 4 Hence, average value of function f A v g = 1 4 ∬ R ( e − 5 y + 3 x ) d x d y 1 4 ∬ R ( e − 5 y + 3 x ) d x d y = 1 4 ∫ 0 2 ∫ 0 2 ( e − 5 y + 3 x ) d x d y Integrate inner integral with respect to x and outer integral with respect to y

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 9.5, Problem 65E

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Average value of function f(x,y)=e−5y+3x over the region R 0≤x≤2,0≤y≤2.

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Chapter 9.5, Problem 64E

Chapter 9.5, Problem 66E

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Average value of function f ( x , y ) = e − 5 y + 3 x over the region R 0 ≤ x ≤ 2 , 0 ≤ y ≤ 2 .

Solution Summary: The author calculates the average value of function f(x,y)=e-5y+3x over a region R where A is the area covered by region

Concept explainers

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To find:

Average value of function f(x,y)=e−5y+3x over the region R 0≤x≤2,0≤y≤2.

Want to see the full answer?

Chapter 9 Solutions

Average value of function f ( x , y ) = e − 5 y + 3 x over the region R 0 ≤ x ≤ 2 , 0 ≤ y ≤ 2 .

Solution Summary: The author calculates the average value of function f(x,y)=e-5y+3x over a region R where A is the area covered by region

Concept explainers

Videos

To find: Average value of function f(x,y)=e−5y+3x over the region R 0≤x≤2,0≤y≤2.

Want to see the full answer?

Chapter 9 Solutions

To find:

Average value of function f(x,y)=e−5y+3x over the region R 0≤x≤2,0≤y≤2.