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Quadrature Formulas

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Quadrature Formulas 

formulas for approximating definite integrals by means of the values of the integrand at a finite number of points. The most common quadrature formulas have the form

where x1x2, …, xn are the nodes of the quadrature formula, A1, A2 . . . ,An are its coefficients, and Rn is the remainder term. For example,

where a ≤ ξ ≤ b (trapezoidal rule). Sometimes for mulas for mechanical, or numerical, quadrature are also called quadrature formulas.

REFERENCE

Krylov, V. I. Priblizhennoe vychislenie integralov, 2nd ed. Moscow, 1967.


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Now if f is as above, then we have the one-point and two-points open Newton-Cotes quadrature formulas [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
 
 
 
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