Riemann Integral versus Geometric Series in Natural Logarithmic Calculation: A Strategy to Enhance Student Competency for Sustainable Technology and Innovation

The natural logarithm (ln) function plays a critical role in higher education, particularly in equipping students with advanced problem-solving skills applicable across science, technology, engineering, and mathematics (STEM) disciplines. This study has two primary objectives: first, to explore and compare the derivation of the natural logarithm using the Riemann integral and geometric series methods; and second, to examine the pedagogical implications of these approaches by analyzing student perceptions. Data were collected from 23 students using a questionnaire comprising five items, each scored on a scale of 1 to 10, to evaluate understanding and perception of both methods. Results from a paired t-test indicate that the Riemann integral method is considered superior to the geometric series in terms of conceptual understanding of the ln function (p < 0.001), ease of memorization (p < 0.001), manual computation (p = 0.032), and implementation in computer programming (p < 0.001). However, no significant difference was found between the two methods regarding the perceived difficulty of ln calculation (p = 0.660). Notably, the geometric series was favored for manual computations due to its simplicity