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曲线下面积的近似计算 by Erik Jacobsen

曲线下面积的近似计算 by Erik Jacobsen
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2017-12-30 01:31
函数微积分积分
本范例演示了如何使用多种近似方法计算函数曲线与x轴之间的面积。涉及的核心数学概念包括积分和近似计算。通过使用GeoGebra命令如Point, Function, Textfield, LeftSum, TrapezoidalSum等，可以动态地展示不同近似方法的效果。适合高中及以上学生学习微积分中的积分概念。

GeoGebra 命令及参数

  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