H2M 2019 P1 Q2: Dynamic Exploration of Ellipse and Definite Integral

① This GeoGebra example dynamically demonstrates Question 2 from the 2019 H2M Mathematics Paper 1, involving definite integrals over an elliptical region and graphical transformations. ② Core mathematical concepts include definite integrals, ellipses, exponential functions, subtraction, logic, and dilation transformations. ③ Construction highlights: commands such as Random, Integral, Solutions, Element, and Simplify are used; objects include buttons (button1, button2), ellipses (e, c1, c2, c3), function f, integral value i, area points A, B, C, etc. Interactive sliders or buttons allow users to change parameters and observe how the integral value and shaded area change. ④ Suitable for senior high school or pre-university students to understand the application of definite integrals in computing geometric areas, and to explore the effect of parameter changes on integral results through dynamic interaction. It also serves as a review tool for competition mathematics such as H2M.