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Use Fubini's Theorem to find the double integral defined over the rectangular region R, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. (Use symbolic notation and fractions where needed.) (4x³ + 2x) (4x²y + 2y) dA = R
Find the volume under the graph of z = f(x, y) = 11x² + 6y² and over the given rectangular region 0 ≤ x ≤ 2, 0 ≤ y ≤ 1. (Give an exact answer. Use symbolic notation and fractions where needed.) V =
Let f(x, y) = 4xy² be defined over the rectangular region R defined by 0 ≤ x ≤ 6,0 ≤ y ≤ 4. (a) Find the Riemann sum of f(x, y) over R by partitioning the region into six congruent subsquares with sides Ax; = 2, i = 1, 2, 3 and Ay; = 2, j = 1, 2. Choose the lower left corner of each subsquare as (uk, Uk), k = 1, 2, 3, ..., 6. (Use symbolic notation and fractions where needed.) Σf(uk, Uk) A Ak = k=1 (b) Find the Riemann sum of f(x, y) over the partition used in (a) but choose the lower right corner of each subsquare as (uk, Uk), k = 1, 2, 3, ..., 6. (Use symbolic notation and fractions where needed.) 6 Σf(uk, Uk) A Ak= = k=1