Breve estudo histórico-pedagógico da integral e suas aplicações físicas e geométricas

Nowadays, the failure and dropout rates in the disciplines of di erential and integral calculus in higher education courses show a lot. Knowing this, show some practical and geometric applications of the integral, an end of approximation and familiarization or student of calculus subjects, in addition to de ning the integral through Riemann's ideas. This work addresses only an integral part of the di erential and integral calculus course. Sequential work is the bibliographic character and was used as the main research source, according to the recommended bibliographies for the Di erential and Integral Calculus courses in the engineering courses. Before starting the applications, a brief study was made on the historical development of the integral, as well as a de nition of some prerequisites for understanding the subject, such as a de nite Riemann integral, an inde nite integral and some methods for solving integrals more complex. Finally, we show some applications that use the practical example of the integral, seeking the closest student, according to theories covered in textbooks and in the classroom.