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Area Under a Linear Function

Area Under a Linear Function
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2015-11-27 19:00
FunctionCalculusIntegral
This example demonstrates how the area under a linear function changes by graphing the values of the area. Key mathematical concepts include functions, geometric construction, and integration. GeoGebra commands used include Point, Line, OrthogonalLine, Intersect, Circle, Ray, Polygon, Segment, and more. Suitable for middle school and above students to learn about function graphs and integration.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Point(yAxis) → C
  4. Point(xAxis) → D
  5. Point(xAxis) → E
  6. Point(xAxis) → F
  7. Point(xAxis) → G
  8. Point(xAxis) → H
  9. Point(xAxis) → I
  10. Point(yAxis) → K
  11. Point(yAxis) → L
  12. Point(yAxis) → M
  13. Line(M, xAxis) → a
  14. OrthogonalLine(M, a) → b
  15. Line(E, J) → c
  16. Point(b) → N
  17. Point(b) → O
  18. Point(a) → P
  19. Point(a) → Q
  20. Point(a) → R
  21. Point(a) → S
  22. Point(a) → T
  23. Point(a) → U
  24. Point(a) → V
  25. Point(a) → W
  26. Line(B, K) → d
  27. Line(A, O) → e
  28. Point(a) → Z
  29. OrthogonalLine(Z, c) → f
  30. Intersect(c, f) → A_1
  31. Circle(Z, (m * x(Z))) → g
  32. Intersect(g, f) → B_1, C_1
  33. Ray(M, C_1) → h
  34. Polygon(M, Z, C_1) → poly1, c_1, m_1, z
  35. Circle(A_1, ((m * x(B)) * x(b) / 2)) → k
  36. Circle(A_1, ((m * x(Z)) * x(Z) / 2)) → p
  37. Intersect(p, f) → D_1, E_1
  38. Segment(E_1, A_1) → i
  39. Segment(B, K) → j
  40. Segment(A, O) → l