Programming Consider a continuous function overthe rectangular region with vertices

Chapter 14, Problem 78

(choose chapter or problem)

Programming Consider a continuous function f(x, y) over the rectangular region R with vertices (a, c), (b, c), (a, d), and (b, d), where a < b and c < d. Partition the intervals [a, b] and [c, d] into m and n subintervals, so that the subintervals in a given direction are of equal length. Write a program for a graphing utility to compute the sum

\(\sum_{i=1}^{n} \sum_{j=1}^{m} f\left(x_{i}, y_{j}\right) \Delta A_{i} \approx \int_{a}^{b} \int_{c}^{d} f(x, y) d A\)

where \(\left(x_{i}, y_{j}\right)\) is the center of a representative rectangle in R.

Text Transcription:

sum_{i=1}^{n} sum_{j=1}^{m} f(x_{i}, y_{j}) \Delta A_{i} approx int_{a}^{b} int_{c}^{d} f(x, y) dA

(x_{i}, y_{j})