Reasons For Numerical Integration
There are several reasons for carrying out numerical integration. The integrand f(x) may be known only at certain points, such as obtained by sampling. Some embedded systems and other computer applications may need numerical integration for this reason.
A formula for the integrand may be known, but it may be difficult or impossible to find an antiderivative which is an elementary function. An example of such an integrand is f(x) = exp(−x2), the antiderivative of which (the error function, times a constant) cannot be written in elementary form.
It may be possible to find an antiderivative symbolically, but it may be easier to compute a numerical approximation than to compute the antiderivative. That may be the case if the antiderivative is given as an infinite series or product, or if its evaluation requires a special function which is not available.
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