Intro to Integration: Rectangular and Trapezoidal Approximations

① This interactive GeoGebra example demonstrates the numerical approximation of definite integrals by visualizing left, right, midpoint, and trapezoidal sums under a curve. ② Core mathematical concepts include the geometric meaning of definite integrals, Riemann sums, the trapezoidal rule, and approximation error estimation. ③ Construction highlights: uses Textfield and inputBox for user inputs, Sequence to generate partition points, Element to extract subintervals, and Integral to compute the exact integral value; objects include function f, endpoints a and b, number of subdivisions n, step size dx, various approximation areas (left, right, mid, trape), error displays (err, text series), and buttons (button1, button2) for interaction. ④ Suitable for high school seniors or early college calculus students to grasp the definition of integrals and numerical methods, and also useful for classroom demonstrations by teachers.