Estimating a Population Mean with Riemann Sums and Integrals

This GeoGebra example demonstrates, in a visual way, how to estimate a population mean (expected value) by approximating an integral using upper and lower Riemann sums. The key mathematical ideas are the Riemann-sum approach to integrals, interval partitioning, geometric area interpretation of sums, and the convergence of these approximations toward the integral value. The lesson connects this to commonly used function models such as polynomial and exponential functions, using geometric scaling/dilation to emphasize how rectangle widths/heights change with the partition. Construction-wise, the example includes on-canvas annotation via the object text1 to guide the viewer, while the main visual elements are built from the function graph together with subdivided intervals and the corresponding summed areas (Upper/Lower Sum / Riemann Sum and Integral Calculus themes). Suitable for late high school through early college, especially for introducing integral estimation of means/expectations in calculus or probability & statistics.