The midpoint rule computes an approximation to a definite integral, made by finding the area of a collection of rectangles whose heights are determined by the values of the function.
The Newton-Cotes formulae, also called the Newton-Cotes quadrature rules or simply Newton-Cotes rules, are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally-spaced points.
Romberg's method computes an integral by generating a sequence of estimations of the integral value and then doing an extrapolation.
Simpson's rule can be thought of as a special case of Romberg's method.
The Trapezoidal rule is a closed type Newton-Cotes formula, where the integral interval is evenly divided into N sub-intervals.
There are two types of the Newton-Cotes method: OPEN and CLOSED.
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