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Comparing Left, Right, and Midpoint Riemann Sums

Comparing Left, Right, and Midpoint Riemann Sums
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2014-04-17 06:35
FunctionCalculusIntegral
This example demonstrates how different types of Riemann sums approximate the area under a curve. Key mathematical concepts include Riemann sums, integrals, and functions. Using GeoGebra commands such as LowerSum, UpperSum, and LeftSum, various Riemann sum graphics are constructed. Suitable for high school mathematics education and learning integral concepts.

GeoGebra Commands & Parameters

  1. LowerSum(f, a, b, n) → LowerSum
  2. UpperSum(f, a, b, n) → UpperSum
  3. LeftSum(f, a, b, n) → LeftSum
  4. RectangleSum(f, a, b, n, 1) → RightSum
  5. RectangleSum(f, a, b, n, r) → RectSum
  6. Intersect(f, yAxis, 1) → A
  7. Segment(A, B) → c
  8. Point(f) → C
  9. Point(xAxis) → D
  10. Segment(C, D) → d
  11. Point(c) → E
  12. Point(d) → F
  13. Segment(E, F) → e
  14. RectangleSum(f, a, b, n, 0.5) → MidpSum
  15. Integral(f, 0, 2) → Area

AI Drawing Prompt Reference

Draw the left, right, and midpoint Riemann sums for the function f in the interval [0,2], approximating the area under the curve with different numbers of rectangles. Start by plotting the function, then draw the rectangles for left, right, and midpoint Riemann sums, and finally calculate and display the integral value of the interval.
The prompt above was compiled from the original drawing commands and is for reference only.