Iterative integration-by-parts procedure and its efficacy assessment in the classroom
DOI:
https://doi.org/10.20983/culcyt.2024.3.2.9Keywords:
problem-solving strategy, Leibniz's integral rule, recursive integration by parts, solution method, quantitative assessmentAbstract
In this work, a simple strategy for iteratively applying Leibniz's integration rule from elementary calculus to operational problems was evaluated. Leibniz's integration rule (also known as the “integration by parts formula”) is a relatively simple formula. However, some typical antiderivative calculus problems require applying this formula iteratively. Unfortunately, this process leads to erroneous and time-consuming solutions due to the various applications of Leibniz's rule and the complexity of the calculations. The strategy proposed in this work reduces the time spent obtaining the solutions of those iterative problems. Furthermore, the procedure used is simple, easy to describe algorithmically, and produces faster results. To show the efficiency of this strategy, an experimental study was conducted with a group of undergraduate engineering students at a public university in Mexico. The ability of these students to use elementary rules of integration was demonstrated by a pretest and the group was divided into two subgroups, one of which was taught the traditional Leibniz rule, while the second learned the strategy studied in this work. The results showed that the current approach produces decisively faster results than the traditional method.
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