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.
Read more about this topic: Numerical Integration
Famous quotes containing the words reasons, numerical and/or integration:
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)
“There is a genius of a nation, which is not to be found in the numerical citizens, but which characterizes the society.”
—Ralph Waldo Emerson (1803–1882)
“The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.”
—Herbert Spencer (1820–1903)