Geometric Construction of Cubic Root with Definite Integral Applications

This GeoGebra example demonstrates how to construct cubic roots geometrically and illustrates their mathematical significance through definite integrals. Core mathematical concepts include: cubic root operations, definite integral calculations, symmetry analysis, and applications of sequences and series. Construction details: Using GeoGebra commands including Intersect, Circle, Point, Angle, and Segment to build geometric figures with objects like points Z, B, C, A, angles α, β, γ, δ, and segments d, e, f, presenting the geometric meaning of cubic roots through prism models. Suitable for high school mathematics and university calculus courses, serving as a teaching example for understanding geometric applications of integrals.