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Area Under a Curve by Mark Dabbs

Area Under a Curve by Mark Dabbs
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2017-03-16 18:25
FunctionCoordinate GeometryIntegral
This example demonstrates how to calculate the area under a curve using geometric methods. Key mathematical concepts include integration and function graphs. Dynamic demonstrations are achieved using GeoGebra commands such as Point, Sequence, Polygon, and Integral.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Sequence(Sequence[Polygon[Sequence[((((2^(n) - (((2 * k) - d) * 2^(n - L))) * x(A)) + ((((2 * k) - d) * 2^(n - L)) * x(B))) / 2^(n), f((((2^(n) - (((2 * k) - d) * 2^(n - L))) * x(A)) + ((((2 * k) - d) * 2^(n - L)) * x(B))) / 2^(n))), d, 0, 2]], k, 1, 2^(L - 1)], L, 1, n) → Polygons
  4. Sequence(Sequence[Sequence[((((2^(n) - (((2 * k) - d) * 2^(n - L))) * x(A)) + ((((2 * k) - d) * 2^(n - L)) * x(B))) / 2^(n), f((((2^(n) - (((2 * k) - d) * 2^(n - L))) * x(A)) + ((((2 * k) - d) * 2^(n - L)) * x(B))) / 2^(n))), d, 0, 2], k, 1, 2^(L - 1)], L, 1, n) → PolygonPoints
  5. Sum(Join[Polygons]) → TotalPolygonArea
  6. Point(PolygonPoints) → C
  7. Point(PolygonPoints) → D
  8. Polygon(A, B, C, D) → TrapeziumArea, a, b, c, d
  9. Integral(f, x(A), x(B)) → h
  10. Sequence(Element[Polygons, k, 1], k, 1, n) → PolyAreas
  11. Sequence(2^(k), k, 0, n - 1) → PolyNumber
  12. TableText({PolyNumber, PolyAreas}, "vc|_|") → text1
  13. TableText({Join[Polygons]}, "vc|_|") → AllPolyAreas
  14. Sum(PolyNumber) → SumofPolys