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两曲线绕轴旋转体的体积

两曲线绕轴旋转体的体积
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2018-01-26 08:57
立体几何微积分积分
本范例演示了两曲线绕轴旋转形成的旋转体体积。核心数学概念包括积分和立体几何。通过使用GeoGebra命令如IntegralBetween、Surface、Integral等，可以构造旋转体的体积。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Textfield(f) → inputBox1
  2. Textfield(upperlimit) → inputBox2
  3. Textfield(lowerlimit) → inputBox3
  4. IntegralBetween(f, g, ll, ul) → h_1
  5. Textfield(g) → InputBox1
  6. IntegralBetween(f, g, ll, ul) → AreabyDefiniteIntegral
  7. Surface(u, (f(u) * cos(v)), (f(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfacef
  8. Surface(u, (g(u) * cos(v)), (g(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfaceg
  9. Surface(u, f(u) + (v * (g(u) - f(u))), 0, u, ll, ul, v, 0, 1) → Facexy
  10. Surface(u, ((f(u) + (v * (g(u) - f(u)))) * cos(θ)), ((f(u) + (v * (g(u) - f(u)))) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotate
  11. Surface(ll, (u * cos(v)), (u * sin(v)), u, Min[f(ll), g(ll)], Max[f(ll), g(ll)], v, 0, θ) → LLface
  12. Surface(ul, (u * cos(v)), (u * sin(v)), u, Min[f(ul), g(ul)], Max[f(ul), g(ul)], v, 0, θ) → ULface
  13. Integral(f, ll, ul) → intf
  14. Integral(g, ll, ul) → intg
  15. Surface(u, ((v * f(u)) * cos(θ)), ((v * f(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotatef
  16. Surface(u, ((v * g(u)) * cos(θ)), ((v * g(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotateg
  17. Surface(u, (v * f(u)), 0, u, ll, ul, v, 0, 1) → Facexyf
  18. Surface(u, (v * g(u)), 0, u, ll, ul, v, 0, 1) → Facexyg
  19. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, f(ll), v, 0, θ) → LLfacef
  20. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, g(ll), v, 0, θ) → LLfaceg
  21. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, f(ul), v, 0, θ) → ULfacef
  22. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, g(ul), v, 0, θ) → ULfaceg
  23. Integral(f, ll, ul) → AreabyDefiniteIntegralf
  24. Integral(g, ll, ul) → AreabyDefiniteIntegralg