   Chapter 7.9, Problem 29E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Average Value of a Function over a Region In Exercises 27–30, find the average value of f(x, y) over the region R. f ( x , y ) = x 2 + y 2 R: square with vertices (0, 0), (2, 0), (2, 2), (0, 2)

To determine

To calculate: The average value of f(x,y)=x2+y2 over the region R: square with vertices

(0,0),(2,0),(2,2),(0,2).

Explanation

Given information:

The provided function is f(x,y)=x2+y2.

The region R: rectangle with vertices (0,0),(2,0),(2,2),(0,2).

Formula used:

The average value of integrable function z=f(x,y) over the region R with area A is;

Average value=1ARf(x,y)dxdy

Calculation:

Consider equation of function,

f(x,y)=x2+y2

The region R represents rectangle with vertices (0,0),(2,0),(2,2),(0,2), length 2 units and width 2 units

The area of region R is 4 square units.

Now apply, the formula of the average value of integrable function f(x,y)=x2+y2 over the region rectangle with vertices (0,0),(2,0),(2,2),(0,2) with area 4 units is;

Average value=140202(x2+y2)

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