MathPlotAI Logo MathPlotAI

Exploring Numerical Integration

Exploring Numerical Integration
Loading the math board and drawing, please wait…
2013-04-17 19:33
FunctionSequenceCalculusIntegralSlider Animation
This applet explores three methods of numerical integration: trapezoidal, Simpson's, and rectangular methods. It helps students understand the concept of integration by observing the approximation effects with different step sizes. The applet uses commands like Point, If, Sequence, Element, etc., suitable for high school mathematics education.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a function graph and display three numerical integration methods: trapezoidal, Simpson's, and rectangular. Use a slider to adjust the step size and observe the approximation effects of integration under different step sizes. Mark multiple points on the x-axis and connect them to the function graph with orthogonal lines to form the integration area.
The prompt above was compiled from the original drawing commands and is for reference only.