1. Estimate the volume of the solid that lies below the surface z = xy and above the following rectangle. R = (x, y) | 6 ≤ x ≤ 12, 8 ≤ y ≤ 12 (a) Use a Riemann sum with m = 3, n = 2, and take the sample point to be the upper right corner of each square. (b) Use the Midpoint Rule to estimate the volume of the solid. 2.Calculate the double integral. 10(1 + x^2) / (1 + y^2) dA, R = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 1} R

Question

1. Estimate the volume of the solid that lies below the surface z = xy and above the following rectangle. R = (x, y) | 6 ≤ x ≤ 12, 8 ≤ y ≤ 12

(a) Use a Riemann sum with m = 3, n = 2, and take the sample point to be the upper right corner of each square.

(b) Use the Midpoint Rule to estimate the volume of the solid.

2.Calculate the double integral. 10(1 + x^2) / (1 + y^2) dA, R = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 1} R

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