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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 ) = e x + y

R: triangle with vertices (0, 0), (0, 1), (1, 1)

To determine

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

(0,0),(0,1),(1,1).

Explanation

Given information:

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

The region R: triangle with vertices (0,0),(0,1),(1,1).

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)=ex+y

The region R: triangle with vertices (0,0),(0,1),(1,1).

The area of region R is 12 square units.

Now apply, the formula of the average value of integrable function f(x,y)=ex+y over the region triangle with vertices (0,0),(0,1),(1,1) with area 12 units is

Average value=2010y(ex+y)dxdy

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