How Is the Error Term Derived for Simpson's Rule?

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SUMMARY

The error term for Simpson's Rule is derived using Taylor series expansion. Specifically, the remainder term is expressed as \( R_n = -\frac{(b-a)^5}{90n^4} f^{(4)}(\xi) \), where \( \xi \) is some point in the interval \([a, b]\). This formula indicates that the error decreases rapidly as the number of intervals \( n \) increases, making Simpson's Rule highly accurate for smooth functions. The derivation can be found in detail at the provided link to the Math Fullerton website.

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  • Understanding of calculus, specifically Taylor series expansion
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makethings
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Hi can someone help me find a derivation of the error/remainder term for simpson's rule? None of the 3 math reference textbooks I have at home contain it.
 
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http://math.fullerton.edu/mathews/n2003/SimpsonsRuleMod.html
 
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