   Chapter 15.1, Problem 47E

Chapter
Section
Textbook Problem

Find the average value of f over the given rectangle.47. f(x, y) = x2y, R has vertices (−1, 0), (−1, 5), (1, 5), (1, 0)

To determine

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

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

The average value of given function over the region R is,

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

Given:

The function is f(x,y)=x2y .

The rectangular region, R=[1,1]×[0,5] .

Calculation:

From the given rectangular region it is observed that l=2,b=5 .

Therefore, A(R)=2

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