Chapter 14.2, Problem 51E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Average Value In Exercises 51-56. find the average value of f(x, y) over the plane region R. f ( x , y ) = x R: rectangle with vertices (0, 0), (4. 0), (4, 2), (0, 2)

To determine

To calculate: The average value of f(x,y)=x over the plane region R: rectangle with vertices (0,0),(4,0),(4,2),(0,2).

Explanation

Given:

The provided function is: f(x,y)=x,

R: rectangle with vertices (0,0),(4,0),(4,2),(0,2).

Formula used:

The average value formula is:

AverageÂ value=1Aâˆ¬Rf(x,y)â€‰dA

Calculation:

First find the area of rectangular region R with the bounds 0â‰¤xâ‰¤4 and 0â‰¤yâ‰¤2.

So, the area of region R is,

A=(4)(2)=8

Since, average value of f(x,y) is provided by:

AverageÂ value=1Aâˆ¬Rf(x,y)

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