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Fubini's Theorem Visualization

Fubini's Theorem Visualization
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2017-07-05 20:55
Solid GeometryCalculusIntegralGeometric ConstructionSlider Animation
This example dynamically demonstrates Fubini's theorem, illustrating the interchange of order in double integrals. Key math concepts include integration, volume, solids of revolution, and coordinate transformations. Construction highlights involve Surface, Segment, CurveCartesian commands for modeling regions and solids, with Textfield and Eingabefeld objects for parameterized interaction. Suitable for high school and above students, and calculus instruction.

GeoGebra Commands & Parameters

  1. Textfield(f) → Eingabefeld1
  2. Textfield(vonx) → Eingabefeld2
  3. Textfield(bisx) → Eingabefeld3
  4. Textfield(vony) → Eingabefeld4
  5. Textfield(bisy) → Eingabefeld5
  6. Surface(u, vony, (w * f(u, vony)), u, vonx, bisx, w, 0, 1) → O_1
  7. Surface(bisx, u, (w * f(bisx, u)), u, vony, bisy, w, 0, 1) → O_2
  8. Surface(u, bisy, (w * f(u, bisy)), u, vonx, bisx, w, 0, 1) → O_3
  9. Surface(vonx, u, (w * f(vonx, u)), u, vony, bisy, w, 0, 1) → O_4
  10. Segment((vonx, a, 0), (bisx, a, 0)) → s_1
  11. Segment((bisx, a, 0), (bisx, a, f(bisx, a))) → s_2
  12. Segment((vonx, a, 0), (vonx, a, f(vonx, a))) → s_3
  13. Segment((b, a, 0), (b, a, f(b, a))) → s
  14. CurveCartesian(t, a, f(t, a), t, vonx, bisx) → kurv
  15. Surface(u, a, (w * f(u, a)), u, vonx, bisx, w, 0, 1) → O_y
  16. Surface(u, (0.99 * a), (w * f(u, a)), u, vonx, b, w, 0, 1) → O1_y