Considernbspintrint xy da wherenbsprnbspis the square, Mathematics

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Considernbspintrint xy da wherenbsprnbspis the square

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 R_ij 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.

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Mathematics: Considernbspintrint xy da wherenbsprnbspis the square

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