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Higher order corrected trapezoidal rules in Lebesgue and Alexiewicz spaces
If f :[a,b] → R such that f (n) is integrable then integration by parts gives the formula ∫ b a f (x)dx = (−1)n n! n−1 ∑ k=0 (−1)n−k−1 [ φ (n−k−1) n (a) f (k)(a)−φ (n−k−1) n (b) f (k)(b) ] +En( f ), where φn is a …