Line Integral Visualization: Integrating Along a Parametric Curve

This GeoGebra example demonstrates the concept of a line integral (curve integral) by visualizing the integration of a function along a parametric curve. It shows how the integral accumulates values along the path, often represented as the area under a curve projected onto the path or as a sum of discrete contributions. Core mathematical concepts include definite integrals, line integrals, parametric curves, vector fields, and Riemann sum approximations. The construction uses the CurveCartesian command to define the parametric curve, and the Sequence command to generate a sequence of sample points along the curve. Objects such as f, a, b, n, c, d, e control the function, integration limits, number of subdivisions, and other parameters, while auxiliary objects l1 through l5 (e.g., segments, polygons, or area elements) help visualize the integral sum. This is suitable for university-level calculus or mathematical analysis courses, as well as advanced high school students or teacher demonstrations, providing an intuitive grasp of how line integrals accumulate function values along a path.