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数值积分探索

数值积分探索
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2013-04-17 19:33
函数数列微积分积分滑块动画
本范例通过不同步长探索三种数值积分方法。它展示了梯形法、辛普森法和矩形法的基本原理，帮助学生理解积分的概念。通过调整步长，学生可以观察到不同方法的逼近效果。该范例使用了Point、If、Sequence、Element等GeoGebra命令，适合高中数学教学。

GeoGebra 命令及参数

  1. Point(xAxis) → x_n
  2. Point(xAxis) → x_0
  3. If(c ≟ 0 ∧ IsInteger[(n + 1) / 2], 1, 0) → z
  4. If(z ≟ 0, n) → n_2
  5. If(c ≟ 0, d_1, d) → d_2
  6. Sequence((i, 0), i, a, b, d_2) → L
  7. Element(L, A2) → B1
  8. Element(L, A3) → B2
  9. Element(L, A4) → B3
  10. Element(L, A13) → B12
  11. Element(L, A12) → B11
  12. Element(L, A11) → B10
  13. OrthogonalLine(x_0, xAxis) → p
  14. OrthogonalLine(x_n, xAxis) → q
  15. Element(L, A5) → B4
  16. Element(L, A6) → B5
  17. Element(L, A7) → B6
  18. Element(L, A8) → B7
  19. Element(L, A9) → B8
  20. Element(L, A10) → B9
  21. Element(L, A14) → B13
  22. Element(L, A15) → B14
  23. Element(L, A16) → B15
  24. Element(L, A17) → B16
  25. Element(L, A18) → B17
  26. Element(L, A19) → B18
  27. Element(L, A20) → B19
  28. Element(L, A21) → B20
  29. Element(L, A22) → B21
  30. Element(L, A23) → B22
  31. Element(L, A24) → B23
  32. Element(L, A25) → B24
  33. Element(L, A26) → B25
  34. Element(L, A27) → B26
  35. Element(L, A28) → B27
  36. Element(L, A29) → B28
  37. Element(L, A30) → B29
  38. Element(L, A31) → B30
  39. Element(L, A32) → B31
  40. Element(L, A33) → B32
  41. Element(L, A34) → B33
  42. Element(L, A35) → B34
  43. Element(L, A36) → B35
  44. Element(L, A37) → B36
  45. Element(L, A38) → B37
  46. Element(L, A39) → B38
  47. Element(L, A40) → B39
  48. Element(L, A41) → B40
  49. Element(L, A42) → B41
  50. Element(L, A43) → B42
  51. Element(L, A44) → B43
  52. Element(L, A45) → B44
  53. Element(L, A46) → B45
  54. Element(L, A47) → B46
  55. Element(L, A48) → B47
  56. Element(L, A49) → B48
  57. Element(L, A50) → B49
  58. Segment(B1, (x(B1), f(x(B1)))) → C1
  59. Segment(B2, (x(B2), f(x(B2)))) → C2
  60. Segment(B3, (x(B3), f(x(B3)))) → C3
  61. Segment(B4, (x(B4), f(x(B4)))) → C4
  62. Segment(B5, (x(B5), f(x(B5)))) → C5
  63. Segment(B6, (x(B6), f(x(B6)))) → C6
  64. Segment(B7, (x(B7), f(x(B7)))) → C7
  65. Segment(B8, (x(B8), f(x(B8)))) → C8
  66. Segment(B9, (x(B9), f(x(B9)))) → C9
  67. Segment(B10, (x(B10), f(x(B10)))) → C10
  68. Segment(B11, (x(B11), f(x(B11)))) → C11
  69. Segment(B12, (x(B12), f(x(B12)))) → C12
  70. Segment(B13, (x(B13), f(x(B13)))) → C13
  71. Segment(B14, (x(B14), f(x(B14)))) → C14
  72. Segment(B15, (x(B15), f(x(B15)))) → C15
  73. Segment(B16, (x(B16), f(x(B16)))) → C16
  74. Segment(B17, (x(B17), f(x(B17)))) → C17
  75. Segment(B18, (x(B18), f(x(B18)))) → C18
  76. Segment(B19, (x(B19), f(x(B19)))) → C19
  77. Segment(B20, (x(B20), f(x(B20)))) → C20
  78. Segment(B21, (x(B21), f(x(B21)))) → C21
  79. Segment(B22, (x(B22), f(x(B22)))) → C22
  80. Segment(B23, (x(B23), f(x(B23)))) → C23
  81. Segment(B24, (x(B24), f(x(B24)))) → C24
  82. Segment(B25, (x(B25), f(x(B25)))) → C25
  83. Segment(B26, (x(B26), f(x(B26)))) → C26
  84. Segment(B27, (x(B27), f(x(B27)))) → C27
  85. Segment(B28, (x(B28), f(x(B28)))) → C28
  86. Segment(B29, (x(B29), f(x(B29)))) → C29
  87. Segment(B30, (x(B30), f(x(B30)))) → C30
  88. Segment(B31, (x(B31), f(x(B31)))) → C31
  89. Segment(B32, (x(B32), f(x(B32)))) → C32
  90. Segment(B33, (x(B33), f(x(B33)))) → C33
  91. Segment(B34, (x(B34), f(x(B34)))) → C34
  92. Segment(B35, (x(B35), f(x(B35)))) → C35
  93. Segment(B36, (x(B36), f(x(B36)))) → C36
  94. Segment(B37, (x(B37), f(x(B37)))) → C37
  95. Segment(B38, (x(B38), f(x(B38)))) → C38
  96. Segment(B39, (x(B39), f(x(B39)))) → C39
  97. Segment(B40, (x(B40), f(x(B40)))) → C40
  98. Segment(B41, (x(B41), f(x(B41)))) → C41
  99. Segment(B42, (x(B42), f(x(B42)))) → C42
  100. Segment(B43, (x(B43), f(x(B43)))) → C43
  101. Segment(B44, (x(B44), f(x(B44)))) → C44
  102. Segment(B45, (x(B45), f(x(B45)))) → C45
  103. Segment(B46, (x(B46), f(x(B46)))) → C46
  104. Segment(B47, (x(B47), f(x(B47)))) → C47
  105. Segment(B48, (x(B48), f(x(B48)))) → C48
  106. Segment(B49, (x(B49), f(x(B49)))) → C49
  107. Sum(RemoveUndefined[L_1]) → t
  108. Sum(RemoveUndefined[L_2]) → m
  109. If(IsInteger[(A1 + 1) / 2], F1, 0) → G1
  110. If(IsInteger[(A2 + 1) / 2], F2, 0) → G2
  111. If(IsInteger[(A3 + 1) / 2], F3, 0) → G3
  112. If(IsInteger[(A4 + 1) / 2], F4, 0) → G4
  113. If(IsInteger[(A5 + 1) / 2], F5, 0) → G5
  114. If(IsInteger[(A6 + 1) / 2], F6, 0) → G6
  115. If(IsInteger[(A7 + 1) / 2], F7, 0) → G7
  116. If(IsInteger[(A8 + 1) / 2], F8, 0) → G8
  117. If(IsInteger[(A9 + 1) / 2], F9, 0) → G9
  118. If(IsInteger[(A10 + 1) / 2], F10, 0) → G10
  119. If(IsInteger[(A11 + 1) / 2], F11, 0) → G11
  120. If(IsInteger[(A12 + 1) / 2], F12, 0) → G12
  121. If(IsInteger[(A13 + 1) / 2], F13, 0) → G13
  122. If(IsInteger[(A14 + 1) / 2], F14, 0) → G14
  123. If(IsInteger[(A15 + 1) / 2], F15, 0) → G15
  124. If(IsInteger[(A16 + 1) / 2], F16, 0) → G16
  125. If(IsInteger[(A17 + 1) / 2], F17, 0) → G17
  126. If(IsInteger[(A18 + 1) / 2], F18, 0) → G18
  127. If(IsInteger[(A19 + 1) / 2], F19, 0) → G19
  128. If(IsInteger[(A20 + 1) / 2], F20, 0) → G20
  129. If(IsInteger[(A21 + 1) / 2], F21, 0) → G21
  130. If(IsInteger[(A22 + 1) / 2], F22, 0) → G22
  131. If(IsInteger[(A23 + 1) / 2], F23, 0) → G23
  132. If(IsInteger[(A24 + 1) / 2], F24, 0) → G24
  133. If(IsInteger[(A25 + 1) / 2], F25, 0) → G25
  134. If(IsInteger[(A26 + 1) / 2], F26, 0) → G26
  135. If(IsInteger[(A27 + 1) / 2], F27, 0) → G27
  136. If(IsInteger[(A28 + 1) / 2], F28, 0) → G28
  137. If(IsInteger[(A29 + 1) / 2], F29, 0) → G29
  138. If(IsInteger[(A30 + 1) / 2], F30, 0) → G30
  139. If(IsInteger[(A31 + 1) / 2], F31, 0) → G31
  140. If(IsInteger[(A32 + 1) / 2], F32, 0) → G32
  141. If(IsInteger[(A33 + 1) / 2], F33, 0) → G33
  142. If(IsInteger[(A34 + 1) / 2], F34, 0) → G34
  143. If(IsInteger[(A35 + 1) / 2], F35, 0) → G35
  144. If(IsInteger[(A36 + 1) / 2], F36, 0) → G36
  145. If(IsInteger[(A37 + 1) / 2], F37, 0) → G37
  146. If(IsInteger[(A38 + 1) / 2], F38, 0) → G38
  147. If(IsInteger[(A39 + 1) / 2], F39, 0) → G39
  148. If(IsInteger[(A40 + 1) / 2], F40, 0) → G40
  149. If(IsInteger[(A41 + 1) / 2], F41, 0) → G41
  150. If(IsInteger[(A42 + 1) / 2], F42, 0) → G42
  151. If(IsInteger[(A43 + 1) / 2], F43, 0) → G43
  152. If(IsInteger[(A44 + 1) / 2], F44, 0) → G44
  153. If(IsInteger[(A45 + 1) / 2], F45, 0) → G45
  154. If(IsInteger[(A46 + 1) / 2], F46, 0) → G46
  155. If(IsInteger[(A47 + 1) / 2], F47, 0) → G47
  156. If(IsInteger[(A48 + 1) / 2], F48, 0) → G48
  157. Sum(RemoveUndefined[L_3]) → s
  158. Element(L, A51) → B50
  159. Element(L, A52) → B51
  160. Segment(B50, (x(B50), f(x(B50)))) → C50
  161. Segment(B51, (x(B51), f(x(B51)))) → C51
  162. If(IsInteger[(A49 + 1) / 2], F49, 0) → G49
  163. If(IsInteger[(A50 + 1) / 2], F50, 0) → G50
  164. Textfield(f) → inputBox1

AI 绘图提示语参考

画一个函数图像，并展示三种数值积分方法：梯形法、辛普森法和矩形法。使用滑块调整步长，观察不同步长下积分的近似效果。在x轴上标记多个点，并通过正交线连接这些点与函数图像，形成积分区域。
以上提示语为根据原始绘图命令整理而来，仅供参考。