MathPlotAI Logo MathPlotAI

Curvilinear Integral of a Vector Field Example

Curvilinear Integral of a Vector Field Example
Loading the math board and drawing, please wait…
2017-06-16 21:36
VectorCoordinate GeometrySolid GeometryCalculusIntegral
This example demonstrates the calculation of a vector field's curvilinear integral along a curve in 3D space. Key math concepts include vector fields, curvilinear integrals, derivatives, tangents, and normals. GeoGebra commands/objects used in construction: Polynomial, CurveCartesian, Point, Vector, Tangent, OrthogonalLine, Intersect, Derivative, Segment, Integral, Sequence. Suitable for university students in mathematics or physics, and researchers studying vector fields and curvilinear integrals.

GeoGebra Commands & Parameters

  1. Polynomial({A, B, C, D}) → f
  2. CurveCartesian(t, f(t), t, x(A), x(D)) → γ
  3. Point(γ) → P
  4. Vector(P, P_2) → F
  5. Tangent(P, γ) → t_P
  6. OrthogonalLine(P_2, t_P) → n_t
  7. Intersect(t_P, n_t) → P_3
  8. Vector(P, P_3) → F_p
  9. Derivative(γ) → γ'
  10. Vector(P, P_1) → F_n
  11. Vector(P_1, P_2) → F_{p,1}
  12. Vector(P_3, P_2) → F_{n,1}
  13. Segment(E, D) → h
  14. Integral(y(γ'(x)), x(A), x(D)) → KurvInt
  15. Sequence(Sequence[Vector[(i, j), (i, j - 1.5)], i, -20, 20, 1], j, -20, 20, 2) → Liste1
  16. Vector(P, G) → v