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Trapezoidal Rule

Trapezoidal Rule
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2019-08-19 08:59
FunctionCalculusIntegral
In collections SCIE1000
This example demonstrates the trapezoidal rule, a numerical integration method. It approximates the definite integral by dividing the function graph into multiple trapezoids. Key mathematical concepts include functions, integration, and numerical methods. Commands used include If, Sequence, Max, Min, Textfield, Vector, OrthogonalLine, Sum, and TrapezoidalSum. Suitable for high school math education and learning calculus.

GeoGebra Commands & Parameters

  1. If(a1 ≥ 0, 0.8, 1.1) → View1x
  2. If(a1 ≟ 0, -0.2, a1) → cond2x
  3. If(a ≤ 0, 0.8, 1.1) → View2y
  4. If(a ≟ 0, 0.2, a) → cond2y
  5. Sequence(g(i), i, a1, a, 0.1) → list1
  6. Max(list1) → maxlist1
  7. Min(list1) → minlist1
  8. Textfield(f) → InputBox1
  9. Vector(A, B) → u
  10. Vector(A, C) → v
  11. OrthogonalLine(C, yAxis) → h
  12. OrthogonalLine(B, yAxis) → i
  13. If(y(v) > 0, 0, 1) → condy
  14. If(y(u) < 0, 0, 1) → condx
  15. If(ymin ≟ 0, (ymax * (-0.1)), ymin) → condy2
  16. If(ymax ≟ 0, (ymin * (-0.1)), ymax) → condx2
  17. Textfield(a) → InputBox2
  18. Sequence(a1 + ((k - 1 + d) * dx), k, 1, n) → list2
  19. Sequence((f(Element[list2, i]) * dx), i, 1, n) → list4
  20. Sum(list4) → RiemannSum
  21. If(d ≟ 1, "R", If[d ≟ 0.5, "M", "L"]) → text3
  22. Textfield(n) → InputBox3
  23. Textfield(a1) → InputBox4
  24. Sequence(Polygon[(a1 + ((k - 1) * dx), 0), (a1 + (k * dx), 0), (a1 + (k * dx), f(Element[list2, k])), (a1 + ((k - 1) * dx), f(Element[list2, k]))], k, 1, n) → list3
  25. TrapezoidalSum(f, a1, a, n) → j

AI Drawing Prompt Reference

Draw the trapezoidal approximation of the integral of a function f(x) over the interval [a1, a]. Start by setting the x-axis starting point based on a1, then plot the function graph, divide it into multiple trapezoids, calculate the area of each trapezoid, and sum them up to show the total area.
The prompt above was compiled from the original drawing commands and is for reference only.