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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Bibliographic Details
Main Authors: Julio César Saavedra Vásquez, Márcio Dias de Lima, Duelci Aparecido de Freitas Vaz
Format: Article
Language:English
Published: Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) 2024-12-01
Series:REMAT
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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.
ISSN:2447-2689