Geometric Bounds for a Definite Integral Using Isosceles Triangles and Inscribed

This example demonstrates how to derive upper and lower bounds for a definite integral using a geometric construction and a step (piecewise) function viewpoint. The main math ideas include definite-integral bounding/estimation, relations in isosceles triangles and polygons, and how piecewise/step functions can act as graphical envelopes that approximate the area under a curve. Construction-wise, it uses GeoGebra commands Intersect, Point, Line, Segment, and Polygon to build the key vertices and boundary segments of the geometric configuration; intersections of lines/segments (Intersect) determine critical points. The construction then assembles equation/constraint objects (e.g., eq1, eq2) and parameter-driven quantities (such as i, j, f and the derived f_1, f_2, f_3 together with e_1, e_2) to define the functions or piecewise components used for the integral bounds. It is suitable for advanced high-school enrichment and introductory university calculus, especially for lessons on integral estimates and visually grounded numerical approximation.