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GeoGebra Example: Integral and Logarithm Functions

GeoGebra Example: Integral and Logarithm Functions
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2017-12-30 10:28
FunctionCalculusIntegral
This example demonstrates how to use GeoGebra to plot the relationship between indefinite integrals, natural numbers, logarithmic functions, and geometric mean. It involves core mathematical concepts such as indefinite integrals, natural numbers, logarithms, geometric mean, and rectangles. The construction uses commands like Point, Vector, Textfield, Segment, Line, Derivative, Intersect, Polygon, and Sequence. Suitable for high school and above students to understand the application of calculus and geometric mean.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → f_2
  3. Textfield(f) → inputBox1
  4. Vector(x_1, y_1) → v
  5. Segment(f_a, F) → c
  6. Segment(E, F) → d
  7. Segment(A, x_1) → e
  8. Segment(B, y_1) → g
  9. Segment(B, y_1) → h
  10. Line(x_1, y_1) → i
  11. Textfield(f) → inputBox2
  12. Derivative(f) → q
  13. Segment(C, D) → b
  14. Segment((0, y(A) - δ), (0, y(A) + δ)) → m
  15. Point(m) → G
  16. Point(m) → H
  17. Point(yAxis) → I
  18. Vector(I, J) → u
  19. Intersect(n, p) → K
  20. Intersect(a, p) → L
  21. Intersect(a, r) → M
  22. Intersect(n, r) → N
  23. Polygon(K, L, M, N) → poly1, k_1, l_1, m_1, n_1
  24. Textfield(ε) → inputBox3
  25. Textfield(δ) → inputBox4
  26. Textfield(f) → InputBox1
  27. Sequence((0, xk), xk, y(A) - δ, y(A) + δ, δ / 8) → inx
  28. Sequence(Vector[(0, xk), (2, f(xk))], xk, y(A) - δ, y(A) + δ, δ / 8) → arrowlist