Solution: Approximation In Exercises 14, approximate the integral by dividing the
Chapter 14, Problem 1(choose chapter or problem)
In Exercises 1 - 4, approximate the integral \(\int_{R} \int f(x, y) d A\) by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum \(\sum_{i=1}^{8} f\left(x_{i}, y_{i}\right) \Delta A_{i}\) where \(\left(x_{i}, y_{i}\right)\) is the center of the ith square. Evaluate the iterated integral and compare it with the approximation.
\(\int_{0}^{4} \int_{0}^{2}(x+y) d y d x\)
Text Transcription:
int_R int f(x, y) d A
sum_{i = 1}^{8} f(x_{i}, y_{i}) Delta A_i
(x_i, y_i)
int_{0}^{4} int_{0}^{2} (x + y) dy dx
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