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Fundamental Theorem of Calculus by Malin Christersson

Fundamental Theorem of Calculus by Malin Christersson
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2019-02-25 02:33
FunctionCalculusIntegralGraphing
This example demonstrates the relationship between curves and integrals, illustrating the Fundamental Theorem of Calculus. Key mathematical concepts include integration, functions, and curves. Construction involves using GeoGebra commands like CurveCartesian, Point, OrthogonalLine, and Intersect to create functions, points, perpendicular lines, and their intersections. Suitable for high school students or college freshmen to understand the intuitive representation of the Fundamental Theorem of Calculus.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), t, 1, 9) → a
  2. Point(a) → A
  3. CurveCartesian(t, f(t), t, x(A), 12) → l
  4. Point(xAxis) → C
  5. Point(l) → B
  6. OrthogonalLine(C, xAxis) → g
  7. OrthogonalLine(A, xAxis) → h
  8. Intersect(h, xAxis) → D
  9. OrthogonalLine(A, yAxis) → i
  10. Intersect(i, yAxis) → E
  11. Segment(E, A) → j
  12. OrthogonalLine(B, xAxis) → k
  13. Intersect(k, xAxis) → F
  14. Intersect(k, i) → G
  15. Polygon(D, F, G, A) → q1, d, f_1, g_1, a_1
  16. Integral(f, x(A), x(B)) → c
  17. Integral(f, 1, x(A)) → e