The major goal of this research is to find a numerical method that determines the values of single integrals when they are continuous integrals but their derivatives are not defined at one end of the integral. The error value (correction limits) is additionally calculated using the Lagrange formula, and the method is then contrasted with well-known numerical methods devoid of acceleration techniques. After using accelerated techniques, the procedure delivered excellent results with great precision in condensed time intervals. We labeled it with the letter NK2.