Some Thought on Numerical Integration Based on Interpolation

Abstract

We discuss and do some analysis on numerical integration based on interpolation, midpoint, trapezoidal rule and Simpson rule. We end up with some new formulas, which are not mentioned in numerical analysis textbooks. The strategy we discuss, in terms of pedagogy, illuminate how research on mathematics can be carry out.

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Keywords

numerical integration, midpoint rule, trapezoidal rule, Simpson rule

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