ExamplesRiemannSum

ExamplesRiemannSum - Example of Riemann Sums for f(x) = x2...

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SubInterval [x i-1 , x i ] Sample Point Left Endpoint x i * = x i-1 Height of Rectangle i f(x i *) Length of Rectangle i Δx = x i-1 - x i Area of Rectangle i f(x i *) Δx [ 2, 5 ] x 1 * = 2 f(2) = 2 2 = 4 5 – 2 = 3 4 x 3 = 12 [ 5, 8 ] x 2 * = 5 f(5) = 5 2 = 25 8 – 5 = 3 25 x 3 = 75 [ 8, 11 ] x 3 * = 8 f(8) = 8 2 = 64 11 – 8 = 3 64 x 3 = 192 [ 11, 14 ] x 4 * = 11 f(11) = 11 2 = 121 14 – 11 = 3 121 x 3 = 363 TOTAL AREA = 642 Example of Riemann Sums for f(x) = x 2 on [2,14] with n = 4 subintervals with equal length given by (b-a)/n = (14 – 2)/4 = 3. Sample pts: Left Endpt b 14 4 a f(x)dx = 2 x 2 dx Σ i=1 f(x i *)Δx
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SubInterval [x i-1 , x i ] Sample Point Right Endpt x i * = x i Height of Rectangle i f(x i *) Length of Rectangle i Δx = x i-1 - x i Area of Rectangle i f(x i *) Δx [ 2, 5 ] x 1 * = 5 f(5) = 5 2 = 25 5 – 2 = 3 25 x 3 = 75 [ 5, 8 ] x 2 * = 8 f(8) = 8 2 = 64 8 – 5 = 3 64 x 3 = 192 [ 8, 11 ] x 3 * = 11 f(11) = 11 2 = 121 11 – 8 = 3 121 x 3 = 363
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This note was uploaded on 09/25/2011 for the course CALCULUS 135 taught by Professor Augustarainsford during the Spring '11 term at Rutgers.

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ExamplesRiemannSum - Example of Riemann Sums for f(x) = x2...

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