Two classes of methods for numerical integration are presented
: The class of Newton-Cotes methods and the class
of Gauss methods. In the class of Newton-Cotes methods,
the trapezoidal rule, Simpson's rule and other higher order
rules like Romberg's method have been derived . The
methods are clarified by examples. Mathematica modules
are designed to derive Newton Cotes methods of any accuracy
and to apply them for evaluation of integrals. Gauss
methods are derived in general form with n Gauss-Legendres
knots and in particular with n=1,2,3,4 knots. Example illustrating
the methods are presented. The exact analysis
of both methods of numerical integration has been carrying
out. A set of questions is enclosed in the chapter.
Keywords: Newtons-Cotes formulas, Gauss formulas.
