Chapter 14.2, Problem 52E

### 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 ) = 2 x y R: rectangle with vertices (0, 1), (1, 1), (1, 6), (0, 6)

To determine

To calculate: What the average value of f(x,y)=2xy over the plane region R will be.

Explanation

Given:

f(x,y)=2xy

R: rectangle with vertices (0,1),(1,1),(1,6),(0,6)

Calculation:

Find the area of rectangular region R with the bounds 0â‰¤xâ‰¤1 and 1â‰¤yâ‰¤6.

Area of the region R is,

A=(1)(5)=5

The average value of the function f(x,y) is given by:

AverageÂ value=1Aâˆ¬Rf(x,y)dA

Now, substitute all the values in the aforementioned formula

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