Theorem 14 (Composite Simpson's Method)

Assume [Maple Math] has its 1st, 2nd, 3rd and 4th derivative continuous on [Maple Math] . Then there exists a [Maple Math] in [Maple Math] so that the Composite Simpson's Rule on [Maple Math] subintervals of [Maple Math] can be written as

[Maple Math] .

Here, [Maple Math] .

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Proof

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