Solving problems with integrals for the study of Archimedes' principle in vector physics

Abstract

The  purpose  of  this  article  is  to  analyze  the  vectorial  study  of  Archimedes'  principle using the definite  integral,  establishing  a  connection  between  theoretical  concepts  and  mathematical processes in subjects such as Algebra, Calculus II, Structure of Matter and Educational Evaluation. This  is  a  descriptive  demonstrative  study,  where  the  analysis  is  carried  out  as  part  of  the methodological process for the culmination of students of High School Teachers (PEM in Spanish), focusing on the third year of  the  Mathematical-Physics  course.  To  achieve  this,  the  resolution  of  problems  created  by  the authors is used as a strategy to link theory with practice. The results obtained through this study contribute  to the  enrichment  of  knowledge related  to  Archimedes'  principle  and  are  relevant  for both students and teachers interested in deepening their knowledge on this fundamental topic. In addition, this innovative approach fosters the development of critical thinking in new generations of academics, promoting meaningful and applicable learning in physics and mathematics.