积极 AI Logo 积极 AI

定积分和性质的证明

定积分和性质的证明
几何画板及绘图内容加载中，请稍等……
2018-07-12 05:12
函数微积分积分
该范例演示了定积分和性质的证明过程。核心数学概念包括定积分、微积分。通过使用GeoGebra命令如Integral、Textfield、Point等，构建了函数图像和关键点，展示了定积分的性质。适合高中数学教学和学习。

GeoGebra 命令及参数

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