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Arc Length Estimation and Exact Value of a Function Curve

Arc Length Estimation and Exact Value of a Function Curve
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2015-02-05 04:17
FunctionSequenceCalculusDerivativeIntegral
This example demonstrates estimating the arc length of a function curve by joining equidistant points. It involves core math concepts like derivatives, integrals, sequences, and function graphing. Constructed using GeoGebra commands Sequence, Sum, Textfield, LaTeX, Integral with objects f, a, b, A, B, n, list1, Estimate, list2, inputBox2, text1, Exact, c_1, text2, text3. Suitable for high school and above students learning arc length calculation and numerical estimation techniques.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(a + (i * (b - a) / n), f(a + (i * (b - a) / n))), (a + ((i + 1) * (b - a) / n), f(a + ((i + 1) * (b - a) / n)))], i, 0, n - 1) → list1
  2. Sum(list1) → Estimate
  3. Sequence((a + (i * (b - a) / n), f(a + (i * (b - a) / n))), i, 0, n) → list2
  4. Textfield(f) → inputBox2
  5. LaTeX(Estimate, true, true) → text1
  6. Integral(sqrt(1 + Derivative[f]^(2)), a, b) → Exact
  7. LaTeX(Exact, true, true) → text2

AI Drawing Prompt Reference

Draw a function curve and mark equidistant points on it, connecting these points with line segments to estimate the arc length. Display both the estimated arc length and the exact arc length calculated via integral for comparison.
The prompt above was compiled from the original drawing commands and is for reference only.