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Area Between Two Curves by Tim Brzezinski (2)

Area Between Two Curves by Tim Brzezinski (2)
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2016-08-11 17:35
FunctionCalculusIntegral
In collections BC Calculus
This example demonstrates how to calculate the area between two curves using GeoGebra. Key mathematical concepts include definite integrals and integral calculus. Using commands like Point, Line, Intersect, Integral, and IntegralBetween, the construction of two curves and the calculation of the area between them is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(g) → A
  2. Point(h) → B
  3. Line(A, B) → i
  4. Intersect(j, k) → C
  5. Intersect(j, l) → D
  6. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], D) → C'
  7. Integral(((-(x(i) / y(i))) * x) - z(i) / y(i), x(C), x(C')) → b
  8. IntegralBetween(f, ((-(x(i) / y(i))) * x) - z(i) / y(i), x(C), x(C')) → c
  9. Dilate(C, If[1.5 < a ≤ 2.5, 2.5 - a, 0], D) → C'_1
  10. Integral(((-(x(i) / y(i))) * x) - z(i) / y(i), x(C), x(C'_1)) → d
  11. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], D) → C'_2
  12. IntegralBetween(f, ((-(x(i) / y(i))) * x) - z(i) / y(i), x(C), x(C'_2)) → e
  13. Segment(B, D) → m
  14. Segment(A, C) → n