Exercise 1

  1. Estimate the volume of the solid that lies below the surface \(z = xy\) and above the rectangle \(R = \{(x, y) | 0 \le x \le 6, 0 \le y \le 4\}\). Use a Riemann sum with \(m = 3\), \(n = 2\), and take the sample point to be the upper right corner of each square.
  2. Use the Midpoint Rule to estimate the volume of the solid in part (a).