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Trapezoidal rule
This article is about the quadrature rule for approximating integrals. For the implicit trapezoidal rule for solving initial value problems, see Trapezoidal rule (differential equations). For the explicit trapezoidal rule for solving initial value problems, see Heun's method.
The function f(x) (in blue) is approximated by a linear function (in red).
In numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral
Simpson's rule
Simpson's rule can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P(x) (in red).
For Simpson's voting rule, see Minimax Condorcet.
In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals.
The given tabulated function is approximated to be cubic:
x: 0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0
y: 1.23,1.58,2.03,4.32,6.25,8.36,10.23,12.45
[0.6,1.23],[0.8,1.58],[1.0,2.03],[1.2,4.32],[1.4,6.25],[1.6,8.36],[1.8,10.23],[2.0,12.45]
So, Simpsons 1/3 is the best method here.
