Approximation In Exercises 1 4, approximate the integralby dividing the rectangle with

Chapter 14, Problem 1

(choose chapter or problem)

Approximation 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 \(\sum_{i=1}^{8} f\left(x_{i}, \ y_{i}\right) \ \Delta A_{i}\) 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