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Approximating Definite Integrals with Riemann Sums

Approximating Definite Integrals with Riemann Sums
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2018-02-12 12:30
FunctionCalculusIntegralGeometric Construction
This example demonstrates the graphical phenomenon of approximating definite integrals using Riemann sums. It involves core mathematical concepts such as definite integrals, roots, distributions, logarithms, trigonometric functions, and conditional probability. The construction leverages GeoGebra commands/objects like Point, Integral, UpperSum, LaTeX, and LowerSum. It is suitable for high school and above students or teachers studying calculus.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Integral(f, x(A), x(B)) → ACTUAL_{-}INTEGRAL
  4. UpperSum(f, x(A), x(B), n) → UPPER_{-}SUM
  5. LaTeX(UPPER_{-}SUM, true, true) → text1
  6. LaTeX(f, true, true) → text4
  7. LaTeX(UPPER_{-}SUM, true, true) → text5
  8. LowerSum(f, x(A), x(B), n) → LOWER_{-}SUM
  9. LaTeX(LOWER_{-}SUM, true, true) → text2