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Riemann Sum vs Definite Integral

Riemann Sum vs Definite Integral
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2019-02-14 19:52
FunctionCalculusIntegralGeometric Construction
This example demonstrates how Riemann sums approximate definite integrals graphically. It involves core math concepts like Riemann sums, definite integrals, function graphs, and rectangle partitioning. Construction highlights include commands like RectangleSum, Textfield, Integral, Segment, and Sequence from GeoGebra. Suitable for high school and above learning calculus and integral concepts.

GeoGebra Commands & Parameters

  1. RectangleSum(f_1, a, b, Rectangles, int) → e
  2. Textfield(f_1) → InputBox1
  3. Textfield(a) → InputBox2
  4. Textfield(b) → InputBox3
  5. Textfield(c) → InputBox4
  6. Integral(f_1, a, b) → d
  7. Segment(A, C) → Δx
  8. Sequence(a + (dx * int) + (dx * i), i, 0, Rectangles) → list1
  9. Sequence((Element[list1, i], 0), i, 1, Rectangles) → list2
  10. Sequence((Element[list1, i], f_1(Element[list1, i])), i, 1, Rectangles) → list3
  11. Sequence(Segment[Element[list2, i], Element[list3, i]], i, 1, Rectangles) → list4