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Calculating the Centroid of an Area

Calculating the Centroid of an Area
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2018-10-25 23:15
FunctionIntegralGeometric Construction
This example demonstrates how to calculate the centroid of an irregular shape, combining geometry and calculus concepts. Construction involves GeoGebra commands like Point, LowerSum, and Integral. Suitable for high school or undergraduate students learning basic geometry and calculus.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. LowerSum(f, a, b, n) → US
  4. Sequence((a + Δx / 2 + (k * Δx), f(a + (k * Δx)) / 2), k, 0, n - 1) → L_P
  5. Integral(f, a, b) → c
  6. Segment(S_1, S) → s_1
  7. Segment(S_2, S) → s_2
  8. Sequence(Segment[(0, y(L_P(j))), L_P(j)], j, 1, Length[L_P]) → L_1
  9. Sequence(Segment[(x(L_P(j)), 0), L_P(j)], j, 1, Length[L_P]) → L_2
  10. Surface((u, (w * f(u)), 0), w, 0, 1, u, a, b) → flaeche
  11. Rotate(flaeche, (-α), yAxis) → flaeche'
  12. Rotate(flaeche, β, xAxis) → flaeche'_1
  13. Rotate(S, (-α), yAxis) → S'
  14. Rotate(S, β, xAxis) → S'_1
  15. Segment(S_2, S') → g
  16. Segment(S_1, S'_1) → h