ABSTRACT

We start with the basic concepts of Riemann integration and present numerical method for evaluating certain integrals by replacing the integrands by approximating functions, develop the method of the Riemann sums, and discuss interpolatory quadrature rules for computing the definite integral Iba(f) ≡

∫ b

a f(x) dx. We discuss inter-

polatory quadrature formulas in their basic and repeated (extended or compound) forms, and some of the extensions which are known as the Romberg’s and Gregory’s schemes. We also present quadrature rules which use nodes outside the interval of integration. The error bounds for all quadrature rules are presented, and some iterative and adaptive schemes are analyzed.