Análise numérica e modos de cálculo aproximado de áreas e volumes

Abstract

In this work, we comprehensively address the importance of numerical techniques in estimating areas and volumes in various situations. We emphasize the relevance of these techniques in complex contexts where direct approaches are impractical or inaccessible. Numerical analysis, through mathematical and computational approaches, plays a crucial role in determining areas and capacities, especially in challenging geometries. The text explores the integration of skills related to the teaching of areas and volumes throughout Basic Education, aligned with the National Curricular Base (BNCC). In the scope of numerical analysis, fundamental concepts are presented from an accessible standpoint. Among these concepts are the definite integral, numerical integration methods, numerical error, and convergence, which are essential for the efficient calculation of areas and volumes. Furthermore, specific methods are discussed, such as the rectangle method, trapezoidal method, and Simpson's rule for areas, as well as methods involving crosssectional areas and cylindrical shells for volumes. The article also proposes the investigation and comparison of numerical methods, aiming to contribute to the appropriate selection of these techniques in different applied contexts. In summary, this work provides a comprehensive view of the importance of numerical techniques in estimating areas and volumes, highlighting their applicability in challenging situations and offering a solid foundation for the selection and application of these techniques in various educational and practical contexts.