Education On Building A Flat In (Determinants Of Matrix, Definite Integrals, And Discriminatory)

Abstract

This paper examines the calculation of plane areas using three mathematical approaches: matrix determinants, definite integrals, and discriminants. Although determinants are commonly studied in linear algebra and definite integrals in calculus, both concepts are closely related in solving area problems. The study aims to compare the results, efficiency, and applicability of these methods for calculating the areas of closed polygons, including triangles, squares, parallelograms, kites, and trapezoids, as well as regions bounded by the intersection of two quadratic functions. This research employs a literature review method through the analysis of books, journal articles, and other scientific references relevant to matrix determinants, definite integrals, and discriminants. The findings indicate that the determinant and definite integral methods produce identical area values for linearly bounded polygons, while the discriminant and definite integral methods yield equivalent results for regions formed by the intersection of quadratic functions. The determinant and discriminant methods offer greater computational efficiency in specific cases, whereas the definite integral method provides broader applicability for both linear and nonlinear boundaries. These findings contribute to mathematical visualization and can be utilized as instructional materials to strengthen students’ understanding of area concepts in linear algebra and calculus courses.