Centroid of a Parametric Curve

This GeoGebra worksheet demonstrates the dynamic computation of the centroid (center of mass) of a parametric curve. The centroid is calculated using the formulas \(\bar x = \frac{\int x(t)\,ds/dt\,dt}{L}, \quad \bar y = \frac{\int y(t)\,ds/dt\,dt}{L}\) where \(ds/dt = \sqrt{(dx/dt)^2 + (dy/dt)^2}\). The curve is defined with the CurveCartesian command, the integrals are evaluated numerically by NIntegral, and LaTeX is used to display the formulas. Interactive InputBoxes allow users to change curve parameters a, b, k, while a slider and an animation button animate the parameter t, showing a point moving along the curve and the resulting centroid point C with its coordinates \(\bar x, \bar y\). This example is suitable for high‑school or undergraduate calculus courses, providing a visual and computational insight into the concept of the centroid of a parametric curve.