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 ) = 6 x y + 2 x and region 2 ≤ x ≤ 5 , 1 ≤ y ≤ 3 Area covered by region A = 3 × 2 = 6 Hence, the average value of function f A v g = 1 6 ∬ R ( 6 x y + 2 x ) d x d y 1 6 ∬ R ( 6 x y + 2 x ) d x d y = 1 6 ∫ 1 3 ∫ 2 5 ( 6 x y + 2 x ) d x d y Integrate inner integral with respect to x and outer integral with respect to y 1 6 ∫ 1 3 ∫ 2 5 ( 6 x y + 2 x ) d x d y = 1 6 ∫ 1 3 [ ∫ 2 5 ( 6 x y + 2 x

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.5, Problem 63E

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Average value of function f(x,y)=6xy+2x over the region R 2≤x≤5,1≤y≤3.

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Chapter 9.5, Problem 61E

Chapter 9.5, Problem 64E

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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Average value of function f ( x , y ) = 6 x y + 2 x over the region R 2 ≤ x ≤ 5 , 1 ≤ y ≤ 3 .

Solution Summary: The author calculates the average value of function f(x,y)=6xy+2x over the region R.

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To find:

Average value of function f(x,y)=6xy+2x over the region R 2≤x≤5,1≤y≤3.

Want to see the full answer?

Chapter 9 Solutions

Average value of function f ( x , y ) = 6 x y + 2 x over the region R 2 ≤ x ≤ 5 , 1 ≤ y ≤ 3 .

Solution Summary: The author calculates the average value of function f(x,y)=6xy+2x over the region R.

Concept explainers

Videos

To find: Average value of function f(x,y)=6xy+2x over the region R 2≤x≤5,1≤y≤3.

Want to see the full answer?

Chapter 9 Solutions

To find:

Average value of function f(x,y)=6xy+2x over the region R 2≤x≤5,1≤y≤3.