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 2 x + y and region 1 ≤ x ≤ 2 , 2 ≤ y ≤ 3 Area covered by region is A = 1 × 1 = 1 Hence, average value of function f A v g = 1 1 ∬ R ( e 2 x + y ) d x d y ∬ R ( e 2 x + y ) d x d y = ∫ 2 3 ∫ 1 2 ( e 2 x + y ) 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 66E

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To find:

Average value of function f(x,y)=e2x+y over the region R 1≤x≤2,2≤y≤3.

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Chapter 9.5, Problem 65E

Chapter 9.5, Problem 67E

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Average value of function f ( x , y ) = e 2 x + y over the region R 1 ≤ x ≤ 2 , 2 ≤ y ≤ 3 .

Solution Summary: The author calculates the average value of function f(x,y)=e2x+y over the region R.

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To find:

Average value of function f(x,y)=e2x+y over the region R 1≤x≤2,2≤y≤3.

Want to see the full answer?

Chapter 9 Solutions

Average value of function f ( x , y ) = e 2 x + y over the region R 1 ≤ x ≤ 2 , 2 ≤ y ≤ 3 .

Solution Summary: The author calculates the average value of function f(x,y)=e2x+y over the region R.

Concept explainers

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To find: Average value of function f(x,y)=e2x+y over the region R 1≤x≤2,2≤y≤3.

Want to see the full answer?

Chapter 9 Solutions

To find:

Average value of function f(x,y)=e2x+y over the region R 1≤x≤2,2≤y≤3.