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Area Between Two Curves

Area Between Two Curves
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2020-04-09 10:56
FunctionCalculusIntegral
In collections Calculus - Applications of Integrals - Areas and Volumes
This example demonstrates how to calculate the area between two curves using integration. Key mathematical concepts include calculus and integral calculus. It utilizes commands such as Point, Line, Intersect, Integral, IntegralBetween, and Segment in GeoGebra. Suitable for high school and above students to learn the method of calculating the area between curves.

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