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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| 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 |
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| Online Access: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/7273 |
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| author | Julio César Saavedra Vásquez Márcio Dias de Lima Duelci Aparecido de Freitas Vaz |
| author_facet | Julio César Saavedra Vásquez Márcio Dias de Lima Duelci Aparecido de Freitas Vaz |
| author_sort | Julio César Saavedra Vásquez |
| collection | DOAJ |
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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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| format | Article |
| id | doaj-art-de582a8956054fa68f5aa16a70fd822c |
| institution | Kabale University |
| issn | 2447-2689 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
| record_format | Article |
| series | REMAT |
| spelling | doaj-art-de582a8956054fa68f5aa16a70fd822c2024-12-19T14:43:35ZengInstituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)REMAT2447-26892024-12-0110210.35819/remat2024v10i2id7273Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrationsJulio César Saavedra Vásquez0https://orcid.org/0009-0006-5207-9613Márcio Dias de Lima1https://orcid.org/0000-0003-2782-386XDuelci Aparecido de Freitas Vaz2https://orcid.org/0009-0006-5207-9613Federal Institute of Education, Science, and Technology of Goiás, Goiânia, GO, BrazilFederal Institute of Education, Science, and Technology of Goiás, Goiânia, GO, BrazilFederal Institute of Education, Science, and Technology of Goiás, Goiânia, GO, Brazil 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. https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/7273definite integralinverse functionarea of a symmetry region |
| spellingShingle | Julio César Saavedra Vásquez Márcio Dias de Lima Duelci Aparecido de Freitas Vaz Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations REMAT definite integral inverse function area of a symmetry region |
| title | Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations |
| title_full | Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations |
| title_fullStr | Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations |
| title_full_unstemmed | Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations |
| title_short | Geometric approaches to the properties of the definite integral: enhancing understanding through visual demonstrations |
| title_sort | geometric approaches to the properties of the definite integral enhancing understanding through visual demonstrations |
| topic | definite integral inverse function area of a symmetry region |
| url | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/7273 |
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