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ApproxIntSummary

# ApproxIntSummary - x n-1 f x n | E T | ≤ K b-a 3 12 n 2...

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Simca Bouma Math 126 Summary of Methods of Approximate Integration www-scf.usc.edu/˜bouma www.usc.edu/si Name of rule General form Error term Left endpoint ap- proximation Δ x [ f ( x 0 )+ f ( x 1 )+ f ( x 2 )+ · · · + f ( x n - 1 )] (not covered) Right endpoint ap- proximation Δ x [ f ( x 1 )+ f ( x 2 )+ f ( x 3 )+ · · · + f ( x n )] (not covered) Midpoint Rule Δ x [ f ( ¯ x 1 )+ f ( ¯ x 2 )+ f ( ¯ x 3 )+ · · · + f ( ¯ x n )] where ¯ x i = x i - 1 + x i 2 | E M | ≤ K ( b - a ) 3 24 n 2 where K ≥ | f 00 ( x ) | on [ a, b ]. Trapezoid Rule Δ x 2 [ f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + · · ·
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Unformatted text preview: x n-1 ) + f ( x n )] | E T | ≤ K ( b-a ) 3 12 n 2 where K ≥ | f 00 ( x ) | on [ a,b ]. Simpson’s Rule (only for even n ) Δ x 3 [ f ( x )+4 f ( x 1 )+2 f ( x 2 )+4 f ( x 3 )+ ··· + 2 f ( x n-2 ) + 4 f ( x n-1 ) + f ( x n )] | E S | ≤ L ( b-a ) 5 180 n 4 where L ≥ | f (4) ( x ) | on [ a,b ]....
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