Probability Density Function: Area Interpretation via Integral

This GeoGebra example demonstrates how a probability density function (PDF) represents a distribution and how the probability over an interval corresponds to the area under its curve. It emphasizes the geometric meaning of integration by approximating the integral with Riemann-sum style “lower sums” on a selected domain. Key concepts include probability density functions, graphing a function to visualize distribution, and using calculus (integral/area) to compute probabilities from continuous models. Construction-wise, it uses GeoGebra commands such as Integral for the exact computation and LowerSum together with Segment to build interval partitions and the under-approximation area. It also employs objects like Point and Intersect to mark boundaries/critical intersections, and uses function/curve objects (e.g., f, g, h) plus coordinate bounds (xmin/xmax, ymin/ymax) and on-graph text annotations to organize the visualization. Suitable for high-school advanced probability, introductory undergraduate probability/statistics, and calculus-integral interpretation lessons.