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Curvilinear Integral of a Vector Field in IR³

Curvilinear Integral of a Vector Field in IR³
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2017-07-05 19:44
VectorCoordinate GeometryCalculusIntegralParametric Equation
This example demonstrates how to compute the curvilinear integral of a vector field in three-dimensional space. Key mathematical concepts include vector fields, curvilinear integrals, parametric equations, derivatives, and vector operations. GeoGebra commands and objects used in the construction include Sequence, Textfield, CurveCartesian, Derivative, LaTeX, Vector, Line, OrthogonalPlane, Intersect, and Segment. Suitable for university-level mathematics students or learners needing to understand vector field integrals.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[Vector[(xx, yy, zz), (xx, yy, zz) + (F_x(xx, yy, zz), F_y(xx, yy, zz), F_z(xx, yy, zz))], xx, -3, 3], yy, -3, 3], zz, -3, 3) → LVectors
  2. Textfield(F_x) → Textfeld1
  3. Textfield(F_y) → Textfeld2
  4. Textfield(F_z) → Textfeld3
  5. CurveCartesian(cos(t), sin(t), t / 2, t, a, b) → γ
  6. Derivative(γ) → γ'
  7. LaTeX(γ, true, true) → Text4
  8. Textfield(γ) → Eingabefeld1
  9. Textfield(a) → Eingabefeld2
  10. Textfield(b) → Eingabefeld3
  11. Vector(A, B) → VF
  12. Line(A, C) → f
  13. OrthogonalPlane(B, f) → c
  14. Intersect(f, c) → E
  15. Vector(A, E) → par
  16. Vector(A, F) → nor
  17. Segment(E, B) → g
  18. Segment(B, F) → h
  19. Vector(A, A + γ'(t_1)) → rv