Chapter 14.1, Problem 18ES

(a) Let $f\left(x,y\right)=x-2y,$ and as shown in Exercise 17, let the rectangle $R=\left[0,2\right]\times \left[0,2\right]$ be subdivided into 16 subrectangles. Take $\left(x_k^{*},y_k^{*}\right)$ to be the center of the $k\text{th}$ rectangle, and approximate the double integral of $f$ over $R$ by the resulting Riemann sum.

(b) Compare the result in part (a) to the exact value of the integral.