Integral and Derivatives Lesson

① This GeoGebra example dynamically illustrates the relationship between integrals and derivatives, showing how accumulated area and tangent slopes connect. ② Core math concepts include the derivative (instantaneous rate of change), the definite integral (accumulated area), and the Fundamental Theorem of Calculus, with auxiliary visualizations using polygons, scatter plots, and spheres. ③ Construction highlights: uses If and Element commands on lists (list1, list2, list3), defines functions f and g, creates points A through H, adds text labels (text1-text6), inserts an image (pic1), and uses a slider (a) to animate changes, making the integral area and derivative tangent lines interactive. ④ Suitable for high school to early college calculus instruction, ideal for classroom demonstrations, self-study, or review, bridging abstract concepts with geometric intuition.