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Visualizing the Mean Value Theorem for Integral and its Proofs

Visualizing the Mean Value Theorem for Integral and its Proofs
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2018-07-17 09:59
FunctionCalculusIntegralGeometric ConstructionGraphing
This example visualizes the Mean Value Theorem for Integrals using mapping diagrams and graphs, outlining the proof. Key math concepts include integrals, averages, and function graphs. GeoGebra commands like Integral, Intersect, Extremum, etc., are used in construction. Suitable for high school and above mathematics learners to understand the theorem and its applications.

GeoGebra Commands & Parameters

  1. Integral(P, a, b) → Intgrl
  2. Intersect(P, e) → A, C
  3. Extremum(P, a, b) → M,
  4. Textfield(P) → inputBox1
  5. Textfield(a) → inputBox2
  6. Textfield(b) → inputBox3
  7. Max({y(M), P(a), P(b)}) → MAX
  8. Min({y(M), P(a), P(b)}) → MIN
  9. Vector(Max_{f}, S_2) → u
  10. Vector(Min_{f}, T_1) → v
  11. Vector(Z_*, U_2) → w
  12. Line(Max_{f}, S_2) → h
  13. Line(U_2, Z_*) → i
  14. Line(T_1, Min_{f}) → j
  15. Vector(C_*, Z_*) → z
  16. Segment(x_a, x_b) → k
  17. Point(yAxis) → X
  18. Vector(X, P_X) → l
  19. Integral(Intgrl / (b - a), a, b) → mvt
  20. Integral(MAX, a, b) → MaxRec
  21. Integral(MIN, a, b) → MinRec
  22. Vector(P_X, CheckX) → r
  23. Polygon({(a, 0), a}) → poly1
  24. Polygon({(a, 0), (a, P(y(X))), (b, P(y(X))), (b, 0)}) → MVRec
  25. Segment(Max_{f}, Min_{f}) → s
  26. Segment(P0, U_2) → t