MathPlotAI Logo MathPlotAI

Double Integration in Polar Coordinates by William Haynes

Double Integration in Polar Coordinates by William Haynes
Loading the math board and drawing, please wait…
2017-05-11 02:00
Coordinate GeometryIntegralGeometric Construction
This example demonstrates double integration in polar coordinates. Key mathematical concepts include polar coordinates, double integrals, and their applications in physics and engineering. Using GeoGebra commands such as CircleArc, Point, Angle, etc., the geometric meaning of double integrals is constructed. Suitable for teaching integral calculus in university mathematics courses.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. CircleArc(A, (1.1, 0), (0, 1.1)) → e
  3. Point(e) → D
  4. Angle((1, 0), A, D) → θ
  5. If(θ < π / 6, (sin((2 * θ)); θ), (cos(θ); θ)) → E
  6. Segment(A, E) → g
  7. Point(Segment[A, R_{max}]) → R
  8. CircleArc(A, (r; 0), (r; 90°)) → d
  9. Ray(A, D) → f
  10. CurveCartesian((sin((2 * θ)); θ), θ, 0, (2 * 3.141592653589793)) → sin2theta
  11. Circle((0.5, 0), 0.5) → costheta
  12. Segment(A, R_{max}) → j
  13. Intersect(d, f) → dA,
  14. CircleArc(A, R_{max}, (0, abs(r'))) → c