Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations
From a purely geometric perspective, this paper provides demonstrations of two properties related to the definite integral. The first one discusses the theorem of the definite integral of a function and its inverse. The second addresses the calculation of the area of a region rotated around the lin...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
2024-12-01
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| Series: | REMAT |
| Subjects: | |
| Online Access: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/7273 |
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| Summary: | From a purely geometric perspective, this paper provides demonstrations of two properties related to the definite integral. The first one discusses the theorem of the definite integral of a function and its inverse. The second addresses the calculation of the area of a region rotated around the line y = x. The intention is to illustrate that when feasible, it is advantageous to explore the geometric aspects of the elements involved in a property for the purpose of its demonstration. In both cases, we assume only the monotonicity and continuity of the function.
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| ISSN: | 2447-2689 |