Numerical integration with problem-based learning: theory, exercises, and applications in engineering

The book Numerical Integration with Problem-Based Learning proposes an innovative and meaningful way of approaching classical numerical integration methods within the context of engineering. Through a balanced combination of theory, practice, and contextualization, the work allows the reader to understand not only the formulas and algorithms that underpin integration, but also their application in solving real problems in the professional environment. The text progressively develops the fundamental methods of integration—Trapezoidal Rule, Simpson 1/3, Simpson 3/8, and Romberg—presenting for each one theoretical foundations, deductions, advantages, limitations, and examples carefully designed under the Problem-Based Learning (PBL) methodology. This structure encourages autonomy, critical thinking, and the application of knowledge in interdisciplinary contexts. In this sense, the work integrates complementary digital resources, such as interactive notebooks in Python and methodological guides, which expand the learning experience through computational experimentation. With a practical and pedagogical approach, the book becomes an essential support tool for students and teachers of engineering, applied sciences, and related areas who are interested in strengthening their analytical and technological skills. This book is an invitation to connect mathematics with reality, promoting active, reflective learning that is consistent with the challenges of contemporary higher education.