Some formulae

The following are all closed Newton-Cotes formulae:

n=1 (Trapezoidal Rule)

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n=2 (Simpson's Rule)

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n=3 (Simpson's three-eights rule)

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n=4

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with, in all cases a value in the integration interval.

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One example of an open Newton-Cotes formula is the Midpoint Rule (n=0):

Notice that the end points of the integration interval are not being used in the formula. This is characteristic of open Newton-Cotes formulae.

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