Visualizing the Definite Integral: Riemann Sums and Limit Approximation

① This interactive GeoGebra example visually demonstrates the geometric meaning of the definite integral as the area under a curve, using rectangles (Riemann sums) to approximate that area. ② Core mathematical concepts include definite integrals, Riemann sums (left, right, upper, lower), limits, area, and the fundamental idea of calculus. ③ Construction details: It employs GeoGebra commands such as Point, Integral, Sum, UpperSum, LowerSum, Segment, and Sequence to create the function f, interval [a,b], upper/lower sum rectangles, area objects, and interactive buttons (e.g., button1, button4) with a slider n controlling the number of subdivisions, dynamically showing how the Riemann sum approaches the integral value as n increases. ④ Suitable for high school to early college calculus courses, this example helps students grasp the definition of the definite integral, the approximation process, and the concept of limits, and is ideal for classroom demonstrations or self-paced exploration.