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Show that the following quadrature rule 3h 3h Ish = f(x) da s 3 (f(0)+31(h) +3f (2h) + f(3h), h> 0, Jo. is fifth

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Show that the following quadrature rule 3h 3h Ish = f(x) da s 3 (f(0)+31(h) +3f (2h) + f(3h), h> 0, Jo. is fifth order accurate in h (the error term is O(h)). (Hint: Use Taylor's expansion at 3h/2).

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