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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 y

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

To determine

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

(0,0),(4,0),(4,2),(0,2).

Explanation

Given information:

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

The region R: rectangle with vertices (0,0),(4,0),(4,2),(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)=xy

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

The region R represents rectangle with vertices (0,0),(4,0),(4,2),(0,2), length 4 units and width 2 units.

The area of region R is 8 square units.

Now apply, the formula of the average value of integrable function f(x,y)=xy over the region rectangle with vertices (0,0),(4,0),(4,2),(0,2)<

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