Cosine Area Function via Riemann Sums

This example visualizes how the “cosine area function” evolves by stacking piecewise rectangles under the cosine curve (on a chosen interval), illustrating how cumulative area depends on the moving upper bound. It connects the graphical approximation of an integral with Riemann sums—specifically upper and lower sums—to show how the true integral is approached as the partition becomes finer. Key math ideas include the cosine function, piecewise step approximations, upper/lower sums or general Riemann sum concepts, and the interpretation of area as an accumulated arithmetic mean–like quantity. In GeoGebra, the construction uses the Integral command with objects representing the function f, interval endpoints a and b, and partition-related sets P and Q (points/subinterval ranges) to compute the running integral/area value, producing the area function from which the geometric behavior can be read directly. Suitable for late secondary school through first-year calculus, particularly for teaching the geometric meaning of integration and numerical approximation.