Area Under a Curve by Dr. Doug Davis, 3D

Area Under a Curve by Dr. Doug Davis, 3D
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2015-09-21 22:26
In collections Fun with Functions
This example demonstrates the approximation of the area under a curve using rectangles, illustrating Riemann sums. Key math concepts include upper and lower sums, left and right Riemann sums. It is constructed using commands like Polynomial, Point, UpperSum, LowerSum, Integral, RectangleSum, and Segment to visualize the approximation process and integral calculation. Suitable for high school calculus education to understand the geometric meaning of definite integrals and the concept of Riemann sums.

GeoGebra Commands & Parameters

  1. Polynomial({C, D, E, F, G}) → g
  2. Point(xAxis) → B
  3. Point(xAxis) → A
  4. UpperSum(g, x(A), x(B), n) → uppersum
  5. LowerSum(g, x(A), x(B), n) → lowersum
  6. Integral(g, x(A), x(B)) → intergral
  7. RectangleSum(g, x(A), x(B), n, 0) → leftSum
  8. RectangleSum(g, x(A), x(B), n, 1) → rightSum
  9. RectangleSum(g, x(A), x(B), n, 0.5) → midSum
  10. Segment(TrueRight, TrueLeft) → d