The table shows values of a function over a square region R. Divide the region into 16 equal squares and select (x i ,

The table shows values of a function ƒ over a square region R. Divide the region into 16 equal squares and select (x_i, y_i) to be the point in the ith square closest to the origin. Compare this approximation with that obtained by using the point in the ith square farthest from the origin.

f*f* f(x, y) dy dx X 0 1 2 3 4 y 0123 4 32 31 28 23 16 31 30 27 15 28 27 24 19 12 22 19 14 7 16 15 12 7 0 23 22