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Riemann Sums 1. Let A be the area of the region bounded by the graph of f (x) = x2 over the interval [1, 3]. a) Use the Right-Hand Rule to set up and simplify the formula for the sum area Rn of n right-hand rectangles: Rn = n X f (a + i∆x)∆x, where ∆x = i=1 b−a n b) Use your formula for Rn to approximate A by n = 5, 10, 100, 1000, and 50,000 rectangles. Present your data in table form (as shown), rounded to three decimal places of accuracy. n Rn 5 10 100 1,000 50,000 c) Find the precise area A by computing the limit A = lim Rn . n→∞ 2. Let A be the area of the region bounded by the graph of f (x) = 2x + 1 over the interval [0, 3]. a) Sketch the graph of f and shade the region at issue. b) Compute A by making an elementary geometric argument.
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