00; 00. 2. CHAPTER 2. NUMERICAL INTEGRATION. BONDS. 58 ~ h2 - (b - a) max Ifl/(x)l, a~x~b 24 since Ifl/(ei,T) I ~ maxa~x~b Ifl/(x)l, for all i = 1 : n. 22) is therefore proven. 30). 26). Recall that any continuous function on a closed interval has a finite maximum, which is achieved at (at least) one point of the interval.
4 or 8 intervals, and compute the numerical approximation of the integral. We then double the number of intervals and compute another approximation of 1. If the absolute value of the difference between the new and old approximations is smaller than the required tolerance tol, we declare the last computed approximation of the integral to be the approximate value of 1 that we are looking for. Otherwise, the number of intervals is again doubled and the process is repeated until two consecutive numerical integration approximations are within the desired tolerance tol of each other.