Numerical Integration
Numerical integration is a computational technique used to approximate the definite integral of a function when an analytical solution is difficult or impossible to obtain. It involves dividing the area under a curve into smaller segments (like rectangles, trapezoids, or using polynomial approximations) and summing their contributions to estimate the total integral. This method is essential in fields such as physics, engineering, finance, and data science where integrals arise from real-world problems.
Developers should learn numerical integration when working with scientific computing, simulations, or data analysis tasks that involve continuous functions without closed-form integrals. It is crucial for solving differential equations, calculating probabilities in statistics, optimizing engineering designs, or processing signals in digital systems. Mastery of this concept enables accurate modeling and prediction in applications ranging from financial derivatives pricing to physical system simulations.