Numerical Integration: Rectangle, Trapezoidal & Simpson Methods
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This GeoGebra example demonstrates three numerical integration methods for approximating definite integrals: the Rectangle Method, Trapezoidal Method, and Simpson Method. Key mathematical concepts include numerical integration, function approximation, partition summation, and error analysis. Construction uses the Sequence command to generate equally spaced partition points, builds left/right rectangle approximation lists (liste1, liste2), draws trapezoidal approximations (liste3, liste4), uses a slider (numb) to control partition number, and displays approximation values (texte1). Ideal for high school math electives or college calculus courses, helping students intuitively understand the geometric meaning and numerical computation of definite integrals.
GeoGebra Commands & Parameters
Sequence((n, 0), n, left, right, step) → liste1Sequence((n, f(n)), n, left, right, step) → liste2Sequence((n + step, f(n)), n, left, right - step, step) → liste4Sequence(Polygon[Element[liste1, i], Element[liste2, i], Element[liste4, i], Element[liste1, i + 1], Element[liste1, i]], i, 1, numb) → liste3