Answer: 3540 The average value or mean value of a continuous functionf(x, y) over a

Chapter 14, Problem 38

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The average value or mean value of a continuous function \(f(x, y)\) over a rectangle \(R=[a, b] \times[c, d]\) is defined as

                                \(f_{\mathrm{ave}}=\frac{1}{A(R)} \iint_{R} f(x, y) d A\)

where \(A(R)=(b-a)(d-c)\) is the area of the rectangle \(R\) (compare to Definition 5.8.1). Use this definition in these exercises.

Find the average value of \(f(x, y)=x\left(x^{2}+y\right)^{1 / 2}\) over the rectangle \([0,1] \times[0,3]\).

Equation Transcription:

Text Transcription:

f(x, y)

R=[a, b]x [c, d]

f_ave=1/A(R) integral integral_R f (x, y) d A

A(R)=(b-a)(d-c)

R

f(x, y)=x(x^2+y)^1/2

[0,1]x [0,3]

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