定积分可加性证明的 GeoGebra 演示

GeoGebra 命令及参数

1. Sequence(1, n) → N1
2. Sequence(0, n) → N0
3. Zip(a - dx / 2 + (k * dx), k, N1) → c_*
4. Zip(a + (k * dx), k, N0) → x_*
5. IndexOf(1, Findc) → c_#
6. Integral(P, a, c) → IPac
7. Integral(P, c, b) → IPcb
8. Integral(P, a, b) → IPab
9. Textfield(P) → inputBox1
10. Point(yAxis) → D
11. Point(yAxis) → E
12. Line(D, E) → Xaxis
13. Line(Ypt, Xaxis) → Yaxis
14. Vector(G, J) → u
15. Vector(I, F) → v
16. Vector(H, K) → w
17. Segment(F, K) → f
18. Segment(F, J) → h
19. Segment(I, H) → i
20. Segment(G, I) → j
21. Integral(αP, a, b) → IαPab
22. Line(M, Yaxis) → Y2axis
23. Vector(J, αs_a) → e
24. Vector(K, αs_b) → d
25. Segment(αs_a, αs_b) → g
26. Segment(J, K) → m
27. Segment(G, H) → p
28. Textfield(Q) → InputBox1
29. Integral(Q, a, b) → IQab
30. Integral(P(x) + Q(x), a, b) → IPQab
31. Line(O, Xaxis) → q
32. Vector(G, SQa) → r
33. Vector(H, SQb) → s
34. Segment(SQb, SQa) → t
35. Vector(K, SPQb) → u_1
36. Vector(SQb, SPQb) → v_1
37. Vector(SQa, SPQa) → w_1
38. Segment(SPQb, SPQa) → f_1
39. Vector(SQb, SQb1) → a_1
40. Segment(SPQb, SQb1) → g_1
41. Segment(SQb1, SPQa) → h_1
42. Vector(J, SQb1) → b_1
43. Point(f_1) → R
44. Zip((0, a + (k * dx)), k, N0) → x_1
45. Zip(Sum[Pcdx_*, k], k, N0) → SPcdx_*
46. Zip(Sum[αPxdx_*, k], k, N0) → SαPcdx_*
47. Zip((x(Ypt), sp), sp, SPcdx_*) → SptPcdx_*
48. Zip(Vector[A, B], A, x_1, B, SptPcdx_*) → vecSP_*
49. Zip((x(M), sp), sp, SαPcdx_*) → SptαPcdx_*
50. Zip(Vector[A, B], A, SptPcdx_*, B, SptαPcdx_*) → vecSαP_*
51. TableText(Transpose[{Join[{{"c_k"}, c_*}], Join[{{"P(c_k)Δx"}, Pcdx_*}], Join[{{"αP(c_k)Δx"}, αPxdx_*}]}], "|_cc") → TableI
52. RectangleSum(P, y(G), y(H), n, 1 / 2) → GrMidEstIntP
53. RectangleSum((α * P(x)), y(G), y(H), n, 1 / 2) → GrMidestIntαP
54. Zip(Sum[Qcdx_*, k], k, N0) → SQcdx_*
55. Zip((x(M), sp), sp, SQcdx_*) → SptQcdx_*
56. Zip(Vector[A, B], A, x_1, B, SptQcdx_*) → vecSQ_*
57. Zip(Sum[PQcdx_*, k], k, N0) → SPQcdx_*
58. Zip((x(O), sp), sp, SPQcdx_*) → SptPQcdx_*
59. Zip(Vector[A, B], A, SptPcdx_*, B, SptPQcdx_*) → vecSP2PQ_*
60. Zip(Vector[A, B], A, SptQcdx_*, B, SptPQcdx_*) → vecSQ2PQ_*
61. RectangleSum(Q, y(G), y(H), n, 1 / 2) → GrMidEstIntQ
62. RectangleSum(PQ, y(G), y(H), n, 1 / 2) → GrMidEstIntPQ
63. Zip((x(O), sp), sp, SQcdx_*) → SptQ'cdx_*
64. Zip(Vector[A, B], A, SptQcdx_*, B, SptQ'cdx_*) → vecSQ'_*
65. Zip((x(O), sp), sp, SPcdx_* + GrMidEstIntQ) → SptP'cdx_*
66. Zip(Vector[A, B], A, SptPcdx_*, B, SptP'cdx_*) → vecSP'_*
67. Vector(G, M_0) → d_1
68. Vector(G, O_0) → e_1
69. TableText(Transpose[{Join[{{"c_k"}, c_*}], Join[{{"P(c_k)Δx"}, Pcdx_*}]}], "|_cc") → TableP
70. Element(x_*, c_# - 1) → c1
71. RectangleSum(P, y(G), c1, c_# - 2, 1 / 2) → GrMidEstIntP1
72. Element(x_*, c_#) → c2
73. RectangleSum(P, c2, y(H), n - c_# + 1, 1 / 2) → GrMidEstIntP2
74. First(c_*, c_# - 2) → c1_*
75. Last(c_*, n - c_# + 1) → c2_*
76. Join({c1_*, {c}, c2_*}) → ca_*
77. Zip(Sum[Pcadx_*, k], k, N0) → SPcadx_*
78. Zip((x(Ypt), sp), sp, SPcadx_*) → SptPcadx_*
79. Zip(Vector[A, B], A, x_1, B, SptPcadx_*) → vecSPa_*