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Trapezium Rule Demonstration

Trapezium Rule Demonstration
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2018-11-27 20:10
FunctionTrigonometryCalculusIntegralGeometric Construction
This example demonstrates the Trapezium Rule for numerical integration, approximating definite integrals by dynamically adjusting intervals and subdivisions; core math concepts include definite integrals, trapezoidal summation, and function graphing; constructed using GeoGebra commands like Integral, Textfield, Sequence, TrapezoidalSum, Function, TableText, If, suitable for high school students and calculus beginners learning numerical integration methods.

GeoGebra Commands & Parameters

  1. Integral(f, a, b) → I
  2. Textfield(f) → inputBox1
  3. Textfield(a) → inputBox2
  4. Textfield(b) → inputBox3
  5. Sequence(a + ((b - a) * i / n), i, 0, n) → L_1
  6. TrapezoidalSum(f, a, b, n) → c
  7. Function(f, a, b) → fShow
  8. TableText({Append["", Sequence[i, i, 0, n]], Append[x, L_1], Append[y, L_y]}, "vc|_") → text4
  9. If(I < c, LaTeX["Overestimate"], LaTeX["Underestimate"]) → text4_1

AI Drawing Prompt Reference

Demonstrate the Trapezium Rule for numerical integration with a function graph and dynamically adjustable subintervals, showing overestimate or underestimate by comparing trapezoidal sum with integral value, and allow dynamic adjustment of intervals and subdivisions, with text annotations for the function, intervals, and results.
The prompt above was compiled from the original drawing commands and is for reference only.