Linear Cross-Section Exercise with Riemann Sums

This example demonstrates how linear cross-sections (secant-style slices) approximate the area under a curve and how those slices can be rotated to visualize the resulting surface. It connects the geometric idea of dividing an interval into n parts with the calculus concept behind upper and lower sums (Upper/Lower Sum and Riemann Sum). The construction emphasizes quadratic (and related) functions, the role of secant lines in creating piecewise linear approximations, and the refinement controlled by the partition parameter n. In GeoGebra, Min/Max are used to determine boundary values or extrema needed for the construction, FitPoly provides polynomial fitting for the curve/shape, Rotate generates the surface from the cross-section geometry, and Point/Line create the key vertices and line segments used as secant lines and interval partitions. The interactive linkage between the function, the sliced cross-sections, and the Surface makes it suitable for teaching introductory calculus, integration approximation, and solid-geometry style visual modeling.