In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. ( See numerical integration for more on quadrature rules.)

For the error of the quadrature formula (1), R(f)= b∫ap(x)f(x)dx−N∑j=1Cjf(xj), there are representations in which the derivative f(r)(x) enters. These representations are of little use for the actual estimation of R(f), since one needs an estimate of the derivative f(r)(x).

The Gaussian quadrature method is an approximate method of calculation of a certain integral . By replacing the variables x = (b – a)t/2 + (a + b)t/2, f(t) = (b – a)y(x)/2 the desired integral is reduced to the form . The Gaussian quadrature formula is. (1)

Gauss quadrature deals with integration over a symmetrical range of x from -1 to + 1. The important property of Gauss quadrature is that it yields exact values of integrals for polynomials of degree up to 2n – 1.

quadrature, in mathematics, the process of determining the area of a plane geometric figure by dividing it into a collection of shapes of known area (usually rectangles) and then finding the limit (as the divisions become ever finer) of the sum of these areas.

b, method = simpson[3/8], opts) command approximates the integral of f(x) from a to b by using Simpson’s 3/8 rule. This rule is also known as Newton’s 3/8 rule….

 Weddle’s Rule is a method of integration, the Newton-Cotes formula with N=6. INTRODUCTION:  Numerical integration is the process of computing the value of definite integral from a set of numerical values of the integrand. The process is sometimes referred as mechanical quadrature.

• Quadrature refers to any method for numerically approximating the value of a definite. integral ∫ b. a f(x)dx. The goal is to attain a given level of precision with the fewest. possible function evaluations.

the act or process of finding a square equal in area to a given surface, especially a surface bounded by a curve. the act or process of finding an area or calculating an integral, especially by numerical methods.