MathPlotAI Logo MathPlotAI

Riemann Sums - Rectangular Approximation (LRAM, RRAM, MRAM)

Riemann Sums - Rectangular Approximation (LRAM, RRAM, MRAM)
Loading the math board and drawing, please wait…
2016-02-07 03:26
FunctionSequenceCalculusIntegral
This GeoGebra example demonstrates the approximation of a definite integral using rectangular sums, with adjustable rectangle counts and bounds. It covers core concepts such as Riemann sums, definite integrals, and limit convergence. The construction utilizes GeoGebra commands including Sequence, Sum, and LaTeX text objects, along with geometric elements like functions, interval endpoints, and rectangle vertices. It is suitable for high school and early college calculus students learning integral approximation.

GeoGebra Commands & Parameters

  1. Sequence(f(i) * h, i, x1 + h / 2, x2 - h / 2, h) → M2
  2. Sequence(f(i) * h, i, x1 + h, x2, h) → R2
  3. Sequence(f(i) * h, i, x1, x2 - h, h) → L2
  4. Sequence((i, f(i)), i, x1, x2, h) → L1
  5. Sequence(Polygon[(x(Element[L1, i]), 0), Element[L1, i], (x(Element[L1, i + 1]), y(Element[L1, i])), (x(Element[L1, i + 1]), 0)], i, 1, n) → LeftP
  6. Sequence(Polygon[(x(Element[L1, i]), 0), (x(Element[L1, i]), y(Element[L1, i + 1])), Element[L1, i + 1], (x(Element[L1, i + 1]), 0)], i, 1, n) → RightP
  7. Sequence((i + h / 2, f(i + h / 2)), i, x1, x2 - h, h) → LM
  8. Sequence(Polygon[(x(Element[L1, i]), 0), (x(Element[L1, i]), y(Element[LM, i])), (x(Element[L1, i + 1]), y(Element[LM, i])), (x(Element[L1, i + 1]), 0)], i, 1, n) → MidP
  9. Sum(L2) → LRAM
  10. Sum(R2) → RRAM
  11. Sum(M2) → MRAM
  12. LaTeX(LRAM, true, true) → text4
  13. LaTeX(RRAM, true, true) → text5
  14. LaTeX(MRAM, true, true) → text6
  15. Textfield(f) → inputBox1
  16. Element(L1, 2) → A