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Parabolic Segment Area Ratio

Parabolic Segment Area Ratio
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2019-06-12 04:29
FunctionCalculusGeometric Construction
This example demonstrates the ratio of area between a parabolic segment and its inscribed rectangle. Key math concepts include parabola, area calculation, definite integral, and similarity transformation. GeoGebra commands used are Root, Integral, Polygon, Intersect, and Segment. Suitable for high school and above students studying calculus and geometric transformations.

GeoGebra Commands & Parameters

  1. Root(f) → A, B
  2. Integral(f, x1, x2) → areay
  3. Polygon(A, (x1, avgy), (x2, avgy), B) → q1, a, g, h, b
  4. Intersect(f, q1) → C, D, E, F, G, H
  5. Segment(D, (x3, 0)) → i
  6. Segment(E, (x4, 0)) → j
  7. Integral(f(x) - avgy, x3, x4) → c
  8. Segment((x3, 0), (x4, 0)) → m
  9. Polygon((x3, 0), (x3, avgy), (x4, avgy), (x4, 0)) → q2, n, p, q, r
  10. Segment((0, avgy), (30, avgy)) → l