Riemann Sum
A Riemann Sum is a mathematical method in calculus used to approximate the definite integral of a function over an interval by dividing the area under the curve into smaller rectangles (or other shapes) and summing their areas. It serves as a foundational concept for understanding integration, providing a way to estimate areas, distances, and other quantities that accumulate continuously. The accuracy of the approximation improves as the number of subdivisions increases, leading to the exact integral in the limit.
Developers should learn Riemann Sums when working on applications involving numerical integration, such as in scientific computing, data analysis, physics simulations, or financial modeling where continuous processes need to be approximated discretely. It is essential for implementing algorithms that compute areas under curves, solve differential equations numerically, or perform Monte Carlo simulations, making it a key skill in fields like machine learning, engineering, and quantitative finance.