Analisis Perbandingan Hasil Integrasi Numerik antara Metode Manual dan Penggunaan Model AI dalam Kaidah Trapesium
DOI:
https://doi.org/10.55606/jutiti.v6i2.7437Keywords:
AI-Assisted Calculation, Chatgpt, Error Analysis, Numerical Integration, Trapezoidal RuleAbstract
The rapid development of artificial intelligence has encouraged the use of large language models as supporting tools for mathematical problem solving, including numerical integration. However, the accuracy and consistency of AI-generated numerical answers still need to be evaluated carefully because each model may produce different outputs under the same prompt. This study aims to compare the accuracy of ChatGPT, Claude, and Gemini in solving numerical integration problems using the composite trapezoidal rule. The research applies a quantitative comparative design involving three types of functions, namely polynomial, exponential, and trigonometric functions. Each model was tested five times for each function using the same prompt, interval, and number of subintervals, with n = 12. Manual calculation using the trapezoidal rule was used as the reference value, and the difference between AI output and manual calculation was measured using percentage error. The manual calculation procedure was written step by step, starting from determining the step size, generating the partition points, evaluating the function values, summing the interior ordinates, and substituting the values into the trapezoidal formula. The results show that ChatGPT achieved the lowest overall average error, followed by Claude and Gemini. The findings indicate that AI models can support numerical computation, but their outputs should be verified through manual procedures or computational tools before being used as final answers.
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