Exercise 4

  1. Estimate the volume of the solid that lies below the surface \(z = 1 + x^2 + 3y\) and above the rectangle \(R = [1, 2] \times [0, 3]\). Use a Riemann sum with \(m = n = 2\) and choose the sample points to be lower left corners.
  2. Use the Midpoint Rule to estimate the volume in part (a).