Left, Right, and Midpoint Sums for Area Estimation

① This example dynamically visualizes how to estimate the area under a curve using left-endpoint, right-endpoint, and midpoint rectangles (Riemann sums), and compares the three approximation methods side by side. ② Core mathematical concepts include numerical approximation of definite integrals, Riemann sums (left, right, midpoint), upper and lower sums, and rectangular area summation, along with error analysis of area estimation. ③ Construction highlights: GeoGebra commands LowerSum, UpperSum, LeftSum, RectangleSum, and Integral are used to generate lower, upper, left, rectangle sums, and the exact integral value; a slider n controls the number of subdivisions; function f is defined; text objects text1 through text12 dynamically display each approximation and the actual area; points A, B, C, D and segments AB, CD help annotate the interval. ④ Suitable for high school to early college students learning calculus, this interactive tool helps understand the geometric meaning of definite integrals and numerical approximation methods, and serves as a classroom demonstration or self-exploration resource for teachers and learners.