Problems solving in the integral calculus and the determination of the area under the curve
In Integral Calculus the classic problem is the determination of the area under the curve, when said region is not expressible in terms of elementary figures. This translates into a multiplicity of problems and exercises that are presented to students in a Calculus course. This article presents a u...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Grupo de Pesquisa sobre Práticas Socioculturais e Educação Matemática (GPSEM)
2024-12-01
|
| Series: | REMATEC. Revista de Matemática, Ensino e Cultura |
| Subjects: | |
| Online Access: | http://rematec.net.br/index.php/rematec/article/view/732 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823861321206071296 |
|---|---|
| author | Juan E. N´apoles Vald´es Maria Nubia Quevedo |
| author_facet | Juan E. N´apoles Vald´es Maria Nubia Quevedo |
| author_sort | Juan E. N´apoles Vald´es |
| collection | DOAJ |
| description |
In Integral Calculus the classic problem is the determination of the area under the curve, when said region is not expressible in terms of elementary figures. This translates into a multiplicity of problems and exercises that are presented to students in a Calculus course. This article presents a useful problem for Mathematics Education, derived from a generalized integral operator, for this we define what we understand by an integrable function in this generalized sense, and the geometric interpretation of a generalized definite integral is presented. The interesting thing about this generalization is that said geometric interpretation is similar to the geometric interpretation of the classical Riemann integral, but not in the xy plane, but in the Ty plane, where T is the kernel of the generalized integral.
|
| format | Article |
| id | doaj-art-31865024981b45369ebbb0fe0b9cc74c |
| institution | Kabale University |
| issn | 1980-3141 2675-1909 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Grupo de Pesquisa sobre Práticas Socioculturais e Educação Matemática (GPSEM) |
| record_format | Article |
| series | REMATEC. Revista de Matemática, Ensino e Cultura |
| spelling | doaj-art-31865024981b45369ebbb0fe0b9cc74c2025-02-09T20:53:41ZengGrupo de Pesquisa sobre Práticas Socioculturais e Educação Matemática (GPSEM)REMATEC. Revista de Matemática, Ensino e Cultura1980-31412675-19092024-12-01195210.37084/REMATEC.1980-3141.2024.n52.e2025005.id732Problems solving in the integral calculus and the determination of the area under the curveJuan E. N´apoles Vald´es0https://orcid.org/0000-0003-2470-1090Maria Nubia Quevedo1https://orcid.org/0000-0002-4137-7408Northeast Normal University Military University Nueva Granada In Integral Calculus the classic problem is the determination of the area under the curve, when said region is not expressible in terms of elementary figures. This translates into a multiplicity of problems and exercises that are presented to students in a Calculus course. This article presents a useful problem for Mathematics Education, derived from a generalized integral operator, for this we define what we understand by an integrable function in this generalized sense, and the geometric interpretation of a generalized definite integral is presented. The interesting thing about this generalization is that said geometric interpretation is similar to the geometric interpretation of the classical Riemann integral, but not in the xy plane, but in the Ty plane, where T is the kernel of the generalized integral. http://rematec.net.br/index.php/rematec/article/view/732Problems solvingintegral calculusarea under the curve |
| spellingShingle | Juan E. N´apoles Vald´es Maria Nubia Quevedo Problems solving in the integral calculus and the determination of the area under the curve REMATEC. Revista de Matemática, Ensino e Cultura Problems solving integral calculus area under the curve |
| title | Problems solving in the integral calculus and the determination of the area under the curve |
| title_full | Problems solving in the integral calculus and the determination of the area under the curve |
| title_fullStr | Problems solving in the integral calculus and the determination of the area under the curve |
| title_full_unstemmed | Problems solving in the integral calculus and the determination of the area under the curve |
| title_short | Problems solving in the integral calculus and the determination of the area under the curve |
| title_sort | problems solving in the integral calculus and the determination of the area under the curve |
| topic | Problems solving integral calculus area under the curve |
| url | http://rematec.net.br/index.php/rematec/article/view/732 |
| work_keys_str_mv | AT juanenapolesvaldes problemssolvingintheintegralcalculusandthedeterminationoftheareaunderthecurve AT marianubiaquevedo problemssolvingintheintegralcalculusandthedeterminationoftheareaunderthecurve |