Chapter 14.2, Problem 3E

Approximation In Exercises 3-6, approximate the integral ${\displaystyle \int {}_R{\displaystyle \int f(x,y)}dA}$ by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum ${\displaystyle \underset{i=1}{\overset{8}{\sum }}f(x_i,y_i)\Delta A_i,}$ where $(x_i,y_i)$ the center of the ith square. Evaluate the iterated integral and compare it with the approximation.

${\displaystyle {\int }_0^4{\displaystyle {\int }_0^2(x+y)dydx}}$