   Chapter 7.9, Problem 27E ### 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 ) = y R: rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3)

To determine

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

(0,0),(5,0),(5,3),(0,3)

Explanation

Given information:

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

The region R: rectangle with vertices (0,0),(5,0),(5,3),(0,3).

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)=y

The region R represents rectangle with vertices (0,0),(5,0),(5,3),(0,3), length 5 units and width 3 units

The area of region R is 15 square units.

Now apply, the formula of the average value of integrable function f(x,y)=y over the region rectangle with vertices (0,0),(5,0),(5,3),(0,3) with area 15 square units is

Average value=11505

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