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Unformatted text preview: pair. Add up the areas A = Δ x 3 [ f ( x i1 ) + 4 f ( x i ) + f ( x i +1 )] under the graph of this quadratic equation (parabola). Z b a f ( x ) dx ∼ S n S n = Δ x 3 [ f ( x ) + 4 f ( x 1 ) + 2 f ( x 2 ) + ··· +2 f ( x n2 ) + 4 f ( x n1 ) + f ( x n )] Error bounds Suppose  f 00 ( x )  ≤ K for a ≤ x ≤ b . If E T is the error in the Trapezoidal Rule and E M is the error in the Midpoint Rule, then  E T  ≤ K ( ba ) 3 12 n 2 and  E M  ≤ K ( ba ) 3 24 n 2 . Error bound for Simpson’s rule Suppose  f (4) ( x )  ≤ K for a ≤ x ≤ b . If E S is the error in Simpson’s Rule, then  E S  ≤ K ( ba ) 5 180 n 4 ....
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 Spring '08
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 Calculus, Approximation, Quadratic equation

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