A contour map is shown for a function f on the square R = [0, 6] cross product [0, 6]. Assume a = 3, b = 6, c = 3, d = 6, e = 10, f = 0, g = 0, h = 20, i = 30, j = 40, k = 20, l = 30, m = 40.
(a) Use the Midpoint Rule with m = n = 2 to estimate the value of the following.
∫∫R f(x, y) dA
(b) Estimate the average value of f.