Discussion of Numerical Integration...
Numerical integration is intrinsically a much more accurate procedure than numerical differentiation.
The basic problem
considered by numerical integration is computing an approximation to a definite integral,
The need for a numerical integration arises for two reasons: First, the function to be integrated may be such that the
integral is too complicated to evaluate or may even be impossible to obtain analytically. Secondly, the function may be described
only by a data array of values, so that a numerical approximation is the only approach available.