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Integrals and Everyday Situations Applied by our AP Calculus Students


The students of our AP Calculus course analyzed and chose different real situations in which areas between curves are involved with integrating integrals and applying concepts seen in class.

Some of the topics were: behavior of birth rates, motor racing, swimming pool design, Gini indices used to measure income inequality, costs and marginal incomes applying them to microeconomics, the behavior of populations and migrations adjusted to the conditions of a country, the cubic curve of Tschirnhaunsen directed to the behavior of radars and design of aircraft wings, among others.

One of our students’ outstanding achievements was finding the connection between integrals with areas of study as diverse as economics, design and architecture, automotive engineering, aeronautical engineering, and population phenomena framed in a social context.

This work goes beyond what is expected, since, in the student submissions, research on the historical context, a real problematic situation, its solution, the interpretation within the parameters of the class, the applicability in a context was evidenced, currently referenced by the same students and their presentation through an infographic.

We invite the community to enjoy the students’ infographics with their respective QR codes and videos of what the students accomplished in this project. We also ask the community to observe this material and consult the QR codes to delve into the solutions provided by our students. We feel very proud of all of their work!

José Luís Zamora AP Calculus Teacher



Resumen: Los estudiantes del curso AP Calculus analizaron y escogieron diferentes situaciones reales en las que se involucran áreas entre curvas con el uso de integrales y aplicación de conceptos vistos en clase. Algunos de los temas son los siguientes: comportamiento de tasas de natalidad, automovilismo, diseño de piscinas, índices de gini utilizados para medir la desigualdad de los ingresos, costos e ingresos marginales aplicándolos a microeconomía, comportamientos de poblaciones y migraciones ajustados  a las condiciones de un país, la curva cúbica de Tschirnhausen dirigido al  comportamiento de radares y diseño de alas de aviones, entre otros.  Uno de los grandes logros fue encontrar la conexión entre el tema de integrales con áreas de estudio tan diversas como economía, diseño y arquitectura, ingeniería automotriz, ingeniería aeronáutica, fenómenos poblacionales enmarcados en un contexto social. Adjuntamos las infografías de los estudiantes con sus respectivos códigos QR y algunos videos de lo que los estudiantes realizaron en este proyecto. Los invitamos a que observen dicho material y consulten los códigos QR para ahondar en las soluciones que dieron los estudiantes. 

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