Estimation of Definite Integral: Rectangle and Trapezoidal Sums

① This GeoGebra example demonstrates numerical estimation of a definite integral by visualizing rectangle sums (RectangleSum) and trapezoidal sums (TrapezoidalSum) approximating the area under a curve. ② The core mathematical concepts are Riemann sums, including left/right rectangle rules and the trapezoidal rule, and the convergence of these approximations to the exact integral as the number of subintervals increases. ③ Construction details: The commands RectangleSum and TrapezoidalSum are used to generate the approximations; objects include the function f, interval endpoints a and b, text objects text1 and text2 for displaying results, and auxiliary objects c, d, e, g likely controlling the number of subintervals or error display. ④ Suitable for high school seniors or early college students learning calculus, useful for understanding the geometric meaning of definite integrals and numerical integration methods, and as a classroom demonstration tool for teachers.