Left and Right Riemann Sums Visualization

① This interactive GeoGebra example visually demonstrates left and right Riemann sums for a given function on a specified interval, illustrating how rectangular approximations approach the definite integral. ② Core mathematical concepts include Riemann sums, definite integrals, interval partitioning, rectangular approximation, and the limit process, fundamental to introductory calculus. ③ Construction details: The applet uses GeoGebra commands such as Point, Sequence, and Take to generate partition points and rectangle heights, CreatePanel for an interactive control panel, and Integral to compute the exact integral value. Objects include leftRect and rightRect for the rectangles, leftSum and rightSum for the sums, along with text1–text6 to display numerical results and explanations. ④ Suitable for high school advanced placement or university calculus courses, enabling students to explore how increasing the number of rectangles n improves approximation accuracy and builds intuition about limits and integration.