?Use the midpoint rule with m = n to show that the average value of a function f on a
Chapter 5, Problem 58(choose chapter or problem)
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))
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer