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Tutorial Exercise
Approximate the integral $\iint_R f(x, y) dA$ by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum $\sum_{i=1}^8 f(x_i, y_i) \Delta A_i$, where $(x_i, y_i)$ is the center of the $i$th square. Evaluate the iterated integral and compare it with the approximation.
$\frac{1}{5} \int_0^4 \int_0^2 x^2y dy dx
