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Example of Piecewise Functions and Indefinite Integrals

Example of Piecewise Functions and Indefinite Integrals
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2020-10-20 06:24
FunctionIntegralGeometric Construction
This example demonstrates the graphical construction of piecewise functions and indefinite integrals, involving key mathematical concepts such as piecewise function definitions, indefinite integral calculations, and geometric plotting techniques. Construction points include using Point, Textfield, Vector, Sequence, and Zip commands to build function graphs, employing Ray and Segment to draw integral regions. Suitable for high school students learning function graphs and integral relationships, or university mathematics courses focusing on geometric applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_x
  2. Textfield(m) → inputBox1
  3. Textfield(s) → inputBoxf
  4. Point(i) → K
  5. Vector(K, s_{inv}D) → w
  6. Vector(s_{inv}D, m_{invSinvD}) → z
  7. Vector(m_{invSinvD}, q_{inv+}) → d
  8. Vector(m_{invSinvD}, q_{inv-}) → f
  9. Vector(q_{inv+}, I) → h_1
  10. Vector(q_{inv-}, J) → j
  11. Textfield(h) → inputBox2
  12. Textfield(b) → inputBox3
  13. Textfield(m_*) → inputBox4
  14. Textfield(m) → inputBox5
  15. Textfield(s) → inputBox6
  16. Point(i) → T_1
  17. Vector(T_1, S_*) → w_1
  18. Vector(S_*, T_*) → u_2
  19. Vector(T_*, R_1) → v_2
  20. Vector(T_*, R_2) → w_2
  21. Vector(R_1, R_#) → a_2
  22. Vector(R_2, R_*) → b_2
  23. Sequence(h - num, h + num) → N
  24. Zip(Vector[(0, i), (2, R(i))], i, N) → QuadRvlist
  25. Zip(Vector[(2, R(i)), (4, q(R(i)))], i, N) → Quadqvlist
  26. Zip(Vector[(4, q(R(i))), (6, m(q(R(i))))], i, N) → Quadmvlist
  27. Zip(Vector[(6, m(q(R(i)))), (8, s(m(q(R(i)))))], i, N) → Quadgvlist
  28. Point(i) → A
  29. Ray(T_1, T_1 + (0, 1)) → g
  30. Ray(S_*, S_* + (0, 1)) → k
  31. Ray(T_*, T_* + (0, m_*)) → p
  32. Ray(R_1, R_1 + (0, 1)) → r
  33. Ray(R_2, R_2 - (0, 1)) → t
  34. Ray(R_#, R_# + (0, 1)) → f_1
  35. Ray(R_*, R_* - (0, 1)) → g_1
  36. Segment(R_1, R_2) → i_1
  37. Segment(R_#, R_*) → j_1

AI Drawing Prompt Reference

Draw a piecewise function and indefinite integral graph by first creating a point A_x on the y-axis, then input the definition of the piecewise function through text fields, use Ray and Segment commands to draw the integral regions, and finally use Sequence and Zip commands to draw the piecewise function graph.
The prompt above was compiled from the original drawing commands and is for reference only.