   Chapter 15.1, Problem 48E

Chapter
Section
Textbook Problem

Find the average value of f over the given rectangle.48. f ( x , y ) = e y x + e y ,   R = [ 0 , 4 ] × [ 0 , 1 ]

To determine

To find: The average value of given function over the region R.

Explanation

Formula used:

fave=1A(R)Rf(x,y)dA , where A(R) is the area of the given rectangular region R.

Given:

The function is f(x,y)=eyx+ey .

The rectangle, R=[0,4]×[0,1] .

Calculation:

From the given rectangle it is observed that l=4,b=1 .

Therefore, A(R)=4.1=4 .

Thus, the average value of the given function is,

fave=140401eyx+eydydx=1404[23

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