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analysis of the simpson rule

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        b a f (t)dt  =  b − a 2n n k=1 [f (x k ) − f (x k−1 )]  x k  = (1 −  k n )  a  +  k n  b    |f (2) (x)| < K 2     b a − b a ≤ K 2 (b − a) 3 12n 2             E (h) :=   h −h f (t)  dt − h[f (−h) − f (h)]  h << 1     E (h) =  E (0) +   h 0 E  (t) dt  =   h 0 [f  (−t) − f  (t)]t dt  0 < t < h << 1   h 0 [f  (−t) − f  (t)] t dt =  f  (−h 1 ) − f  (h 1 ) h 1   h 0 t 2 dt  = −2f  (h 2 ) h 3 3         K 2 (b − a) 3 12n 3  → 0  n  → ∞   f  (x)   [a, b]    K 2  

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