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旋转体体积的计算

旋转体体积的计算
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2016-04-03 07:55
函数立体几何微积分
本GeoGebra范例演示了如何使用盘旋法和壳层法计算绕x轴和y轴旋转的立体体积。用户可以输入函数，观察不同方法下的体积变化。该范例涉及的核心数学概念包括函数、微积分中的积分和旋转体体积计算。通过使用命令如Textfield、Sequence、Surface等，用户可以动态地调整函数和旋转轴，从而更好地理解这些概念。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Textfield(g) → InputBox1
  2. Textfield(ll) → InputBox2
  3. Textfield(ru) → InputBox3
  4. Sequence(ll + (i * ht), i, 0, n) → list1
  5. Surface(f, (2 * π)) → e
  6. Sequence(Cylinder[(list1(i), 0, 0), (list1(i + 1), 0, 0), f(list1(i))], i, 0, n - 1) → listd00
  7. Surface((u * cos(v)), f(u), (u * sin(v)), u, (i * i), ru, v, 0, (2 * π)) → h
  8. Sequence(QuadricSide[Cylinder[(0, f(list1(i)), 0), (0, f(ru), 0), list1(i)]], i, 1, n + 1) → listsy
  9. Sequence(QuadricSide[Cylinder[(list1(i), 0, 0), (ru, 0, 0), f(list1(i))]], i, 1, n + 1) → listsx
  10. Sequence({QuadricSide[Cylinder[(0, f(list1(i)), 0), (0, f(list1(i + 1)), 0), list1(i)]], Bottom[Cylinder[(0, f(list1(i)), 0), (0, f(list1(i + 1)), 0), list1(i)]], Top[Cylinder[(0, f(list1(i)), 0), (0, f(list1(i + 1)), 0), list1(i)]]}, i, 1, n + 1) → listdy
  11. Sequence({QuadricSide[Cylinder[(list1(i), 0, 0), (list1(i + 1), 0, 0), f(list1(i))]], Top[Cylinder[(list1(i), 0, 0), (list1(i + 1), 0, 0), f(list1(i))]], Bottom[Cylinder[(list1(i), 0, 0), (list1(i + 1), 0, 0), f(list1(i))]]}, i, 1, n + 1) → listdx