The methods of numerical integration are used to find approximate values for definite integrals and are useful for the following reasons. It may be that there is no analytical method of finding an antiderivative of the integrand. Possibly, such a method may exist but be very complicated. In another case, the integrand may not be known explicitly; it might be that only its values at certain points within the interval of integration are known. Among the elementary methods of numerical integration are the trapezium rule and Simpson's rule.