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Exploring Integral Calculus to Determine Volumes of Solids Generated by Rotating Simple Curves Using GeoGebra

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Preprints.org
DOI
10.20944/preprints202511.0191.v1

Integral calculus is a fundamental component of mathematics with extensive applications, particularly in computing the volumes of solids of revolution—three-dimensional objects generated by rotating a plane curve around a given axis. This study aims to explore the application of integral calculus in determining the volumes of solids formed by rotating simple curves, supported by GeoGebra as a dynamic visualization tool. A descriptive-exploratory approach was employed, consisting of four main steps: (1) selecting relevant functions and intervals, (2) analytically calculating volume using the disk or shell method, (3) modeling the curve and its rotation in GeoGebra 3D, and (4) verifying and comparing analytical results with the software’s visual estimations. The functions analyzed include y = x2, y = 2x + 1, and y = sin 2 (x) , rotated about both the x-axis and y-axis. Findings indicate that volume values generated by GeoGebra closely align with analytical calculations, with a relative error of less than 1%. Moreover, the interactive three-dimensional visualizations significantly enhance students’ conceptual understanding of integrals by allowing them to observe the geometric formation of solids of revolution and validate their computational results. The integration of analytical methods with digital tools like GeoGebra not only improves computational accuracy but also enriches calculus instruction through intuitive, engaging visual representations that bridge abstract concepts and concrete understanding.

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