MathLiveSimpson's rule
Approximates a definite integral over one interval by fitting a parabola through the endpoints and midpoint of the interval (Simpson's 1/3 rule). It is a standard numerical integration method that is more accurate than the trapezoidal rule for smooth functions.
\int_{a}^{b} f(x)\,dx \approx \frac{b-a}{6}\left[f(a)+4f\left(\frac{a+b}{2}\right)+f(b)\right]What the symbols mean
| lower limit of integration | |
| upper limit of integration | |
| integrand, the function being integrated | |
| integration variable |
About this formula
- FieldMathematics
- TopicNumerical integration
- LevelUniversity
- Also calledSimpson's 1/3 rule, Simpson integration formula, area under curve Simpson, Simpson's 3/8 rule, composite Simpson's rule
- SourceWikidata Q722507
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