ABSTRACT
This chapter deals with the problem of estimating the definite integral. In most cases, the evaluation of definite integrals is either impossible or else very difficult to evaluate analytically. The most important are the ones with degree one, two, and three. However, care must be exercised when using interpolating polynomials of a higher degree; round-off errors and irregularities can cause a problem in these cases. Assuming that no round-off error enters into calculations, the extrapolated values along the diagonal will converge to the correct answer more rapidly than the other values below the diagonal. It is interesting to note that the first and second columns in the array contain estimates obtained respectively by the composite trapezoidal and Simpson’s rules. MATLAB has two built-in functions qad and quadl that use adaptive numerical quadrature to approximate an integral within a specified tolerance.
