Approximating the Area Under a Curve: Rectangle and Trapezoidal Sums

① This interactive GeoGebra example demonstrates how to approximate the area under a curve using rectangle sums and trapezoidal sums, visualizing the geometric meaning of definite integrals. ② Core mathematical concepts include definite integrals, Riemann sums, left/right/midpoint rectangle methods, and the trapezoidal rule, along with the convergence of approximations as the number of partitions increases. ③ Construction highlights: using GeoGebra commands such as Point to define points on the curve, RectangleSum and TrapezoidalSum to generate the sums, and Textfield with an input box (inputBox1) to adjust the number of subintervals n. Objects include the function f, interval endpoints a and b, and variable n, allowing dynamic updates of the approximation. ④ Suitable for high school seniors or early college calculus students to grasp the definition of the integral and numerical integration techniques, and useful for classroom demonstrations by teachers.