?Use the midpoint rule with m = n to show that the average value of a function f on a

Chapter 5, Problem 58

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Use the midpoint rule with m = n to show that the average value of a function f on a rectangular region \(R=[a, b] \times[c, d]\) is approximated by

\(f_{\text {ave }} \approx \frac{1}{n^{2}} \sum_{i, j=1}^{n} f\left(\frac{1}{2}\left(x_{i-1}+x_{i}\right), \frac{1}{2}\left(y_{j-1}+y_{j}\right)\right)\)

Text Transcription:

R=[a, b] \times[c, d]

f_ave approx 1/n^2 sum_i,j=1^n f(1/2 (x_i-1 + x_i), 1/2 (y_j-1 + y_j))

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