Let R be the rectangle given by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and let f(x, y) = x + 5y. We want to estimate the integral ∬f(x, y) dx dy.
a. Divide each side of the rectangle into three equal parts, and for each of the nine squares pick the sample point in the lower left hand corner. Compute the Riemann sum.
b. Use the same subdivision, but now pick your sample points on the upper right of each square. Compute the Riemann sum.
c. How good an estimate for the integral does this give?