Consider the solid that lies above the rectangle (in the xy-plane) R = [-2, 2] X [0, 2] and below the surface z = x2 - 6y + 12.
A) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the largest possible Riemann sum.
B) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the smallest possible Riemann sum.
C) Using iterated integrals, compute the exact value of the volume.