Advanced Numerical and Algorithmic Approaches for Irresolvable Integrals

This fourth volume Advanced Numerical and Algorithmic Approaches for Irreducible Integrals is intended for students researchers and engineers dealing with integrals that cannot be solved analytically. Through a rigorous framework it presents error bounds estimates of maximum achievable precision and methods for determining the optimal number of intervals required. Each numerical technique is illustrated with an algorithm a Python implementation and exercises grounded in diverse application domains such as biology finance and telecommunications. By combining mathematical theory computational tools and real-world case studies the book offers a clear methodological framework for assessing and mastering the precision of numerical methods. This volume completes a four-part series dedicated to both analytical and numerical integration delivering a structured comprehensive and practically oriented vision of integral calculus in the sciences and engineering.