MathPlotAI Logo MathPlotAI

Approximating the Area Under a Curve by Erik Jacobsen

Approximating the Area Under a Curve by Erik Jacobsen
Loading the math board and drawing, please wait…
2017-12-30 01:31
FunctionCalculusIntegral
This example demonstrates various approximation methods for calculating the area between a function curve and the x-axis. Key mathematical concepts include integration and approximation. Using GeoGebra commands such as Point, Function, Textfield, LeftSum, TrapezoidalSum, etc., it dynamically shows the effects of different approximation methods. Suitable for high school and above students learning integral calculus.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Function(f, x(A), x(B)) → g
  4. Textfield(f) → inputBox1
  5. LeftSum(f, x(A), x(B), n) → LeftSum
  6. TrapezoidalSum(f, x(A), x(B), n) → TrapSum
  7. Sequence(Polygon[(x(A) + (k * dx), 0), (x(A) + ((k + 1) * dx), 0), (x(A) + ((k + 1) * dx), f(x(A) + ((k + 1) * dx))), (x(A) + (k * dx), f(x(A) + ((k + 1) * dx)))], k, 0, n - 1) → RightSum
  8. Sequence(Polygon[(x(A) + (k * dx), 0), (x(A) + ((k + 1) * dx), 0), (x(A) + ((k + 1) * dx), f(x(A) + ((k + 1 / 2) * dx))), (x(A) + (k * dx), f(x(A) + ((k + 1 / 2) * dx)))], k, 0, n - 1) → MidSum
  9. Sequence(FitPoly[{(x(A) + (k * dx), f(x(A) + (k * dx))), (x(A) + ((k + 1) * dx), f(x(A) + ((k + 1) * dx))), (x(A) + ((k + 2) * dx), f(x(A) + ((k + 2) * dx)))}, 2], k, 0, n - 2, 2) → SimpSum
  10. Sequence(Integral[Element[SimpSum, k], x(A) + (((2 * k) - 2) * dx), x(A) + ((2 * k) * dx)], k, 1, n / 2) → SimpsonSum
  11. Element(list1, SelectedIndex[methods]) → a
  12. Segment(A, D) → h
  13. Segment(B, E) → i
  14. Integral(f, x(A), x(B)) → farea