DERIVE A NEW RULE FOR FINDING THE VALUES OF NUMERICALLY DEFINED ONE SIDED INTEGRALS (Eureka Journal of Artificial Intelligence and Data Innovation, 2026)
This study's primary objective is to devise a new rule to determine the values of numerically defined fundamentals of continuous functions. Although they are continuous, they are defective in the derivative or defective at one or more points in the integration region.[1] Error formulas were found for them as we deduced this method, where the harmonic mean was taken. For the trapezoid and Simpson methods, then comparing the results with numerical integration methods and adopting the percentage of absolute error, [3]it was found that the new method is better than the previous methods. We concluded that we can rely on this method in calculating definite integrals, as it gave high accuracy in the results.
Keywords: Harmonic Mean, trapezoidal Rule, Simpsonʼs 1/3- rule.