Multiple Integrals

1. Estimate sin (xy) dx dy where R is the square 0 x 1, 0 y 1 by using the Riemann sum corresponding to partition of R in four equal sub squares and with the function evaluated at their centers. Use three decimal places in the calculations. Ans: 0.242

2. Give the Riemann sum approximation of corresponding to the partition of R = {(x, y): 0 x 3, 0 y 3} into nine equal squares and with the integrand evaluated at their centers. Use two-decimal-place accuracy. Ans: 22.62