Consider ∫R∫ xy dA, where R is the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Let us compute some Riemann sums. For any positive integer n we partition R into n2 little squares Rij each with sides 1/n long. Within each little square we evaluate the integrand at the point (x*ij, y*ij), which is the upper right corner.
(a) Find a formula for the Riemann sum
(b) Evaluate the formula
(c) Check your answer by evaluating the iterated integral.