Online calculator: Numerical integration
https://planetcalc.com/5494E.g. 3/8,1,3,3,1 weights can be used for Simpson 3/8 rule. Definite integral approximation with Newton-Cotes integration rules is far from ideal. For real applications, you should use better methods, e.g., the Gauss-Kronrod rule. Hopefully, we'll illustrate it with the new calculators and articles in nearest future.
Simpson's 3/8 Rule -- from Wolfram MathWorld
mathworld.wolfram.com › Simpsons38RuleDec 17, 2021 · Simpson's 3/8 Rule. Let the values of a function be tabulated at points equally spaced by , so , , ..., . Then Simpson's 3/8 rule approximating the integral of is given by the Newton-Cotes -like formula. Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.