Chapter 14.1, Problem 17ES

(a) Let $f\left(x,y\right)=x^2+y,$ and as shown in the accompanying figure, 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.