ICME Integrator III: Dynamic Integral Function Plotter

This example demonstrates a dynamic integral function plotter that visualizes the graph of a function and its integral (antiderivative) in real time. Core mathematical concepts include definite and indefinite integrals, integral functions, derivatives and slopes, and the interplay between function graphs and geometric elements. Construction highlights: using GeoGebra commands such as Point, Integral, Line, Segment, Textfield, Intersect, Slope, Vector, OrthogonalLine, Circle, AngularBisector, Midpoint, Mirror, and CircleSector, the applet builds an interactive interface with objects like function f, integral curve I, tangent lines, slope triangles, and dynamic text fields. Suitable for calculus instruction at high school and undergraduate levels, helping students intuitively grasp the relationship between integrals and areas, slopes and derivatives, and how dynamic parameter changes affect integral results.