旋转区域生成体积的GeoGebra范例

GeoGebra 命令及参数

1. Sequence(Cylinder[(2, g(((k + p) * h)), 0), (2, f(((k + p) * h)), 0), 2 - ((k + 1) * h)], k, 0, m - 1) → CI
2. Sequence(If[Defined[Element[CI, k]], Volume[Element[CI, k]], 0], k, 1, m) → VCI
3. Sequence(Cylinder[(2, g(((k + p) * h)), 0), (2, f(((k + p) * h)), 0), 2 - (k * h)], k, 0, m - 1) → CO
4. Sequence(If[Defined[Element[CO, k]], Volume[Element[CO, k]], 0], k, 1, m) → VCO
5. Rotate(f_1, α, a) → f_3
6. Rotate(g_1, α, a) → g_3
7. Max({0, m - 1}) → DK
8. Surface(((2 - u) * (-cos(β))) + 2, g(((DK + p) * h)), ((2 - u) * sin(β)), u, (DK * h), ((DK + 1) * h), β, 0, α) → Bottom1
9. Surface(((2 - ((DK + 1) * h)) * (-cos(β))) + 2, v, ((2 - ((DK + 1) * h)) * sin(β)), v, g(((DK + p) * h)), f(((DK + p) * h)), β, 0, α) → InnerSurface1
10. Surface(((2 - (DK * h)) * (-cos(β))) + 2, v, ((2 - (DK * h)) * sin(β)), v, g(((DK + p) * h)), f(((DK + p) * h)), β, 0, α) → OuterSurface1
11. Surface(((2 - u) * (-cos(β))) + 2, f(((DK + p) * h)), ((2 - u) * sin(β)), u, (DK * h), ((DK + 1) * h), β, 0, α) → Top1
12. Polygon({((DK * h), g(((DK + p) * h))), (((DK + 1) * h), g(((DK + p) * h))), (((DK + 1) * h), f(((DK + p) * h))), ((DK * h), f(((DK + p) * h)))}) → Rectangle1
13. Rotate(Rectangle1, α, a) → RotatedRectangle1
14. Vector((2, g(((DK + p) * h)), 0), (((DK + p) * h), g(((DK + p) * h)))) → V
15. Rotate(V, α, a) → R'
16. Rotate(A, α, a) → A'
17. Rotate(B, α, a) → B'
18. Vector(A, B) → U
19. Vector(A', B') → H'
20. Integral(((2 - x) * (f(x) - g(x))), 0, 2) → a_1
21. Sum(VCO - VCI) → VolShellSum
22. Sequence(Polygon[((k * h), g(((k + p) * h))), (((k + 1) * h), g(((k + p) * h))), (((k + 1) * h), f(((k + p) * h))), ((k * h), f(((k + p) * h)))], k, 0, m - 1) → Rectangles
23. If(togV ≟ 1, "Hide integral & shell approx", "Show integral & shell approx") → ShowVolumeIntegral
24. Rotate(Rectangles, α, a) → Rectangles'
25. If(togR ≟ 1, "Show One Shell", "Show All Shells") → ShowOneShell
26. Surface(((2 - u / 2) * cos(β)) + 2, u, ((2 - u / 2) * sin(β)), u, 0, 4, β, 0, (2 * π)) → Outer
27. Surface(((2 - sqrt(u)) * cos(β)) + 2, u, ((2 - sqrt(u)) * sin(β)), u, 0, 4, β, 0, (2 * π)) → Inner
28. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
29. Sequence(Surface[2 - ((2 - (k * h)) * cos(β)), (v * f(((k + p) * h))) + ((1 - v) * g(((k + p) * h))), ((2 - (k * h)) * sin(β)), v, 0, 1, β, 0, α], k, 0, m - 1) → Outers
30. Sequence(Surface[2 - ((2 - ((k + 1) * h)) * cos(β)), (v * f(((k + p) * h))) + ((1 - v) * g(((k + p) * h))), ((2 - ((k + 1) * h)) * sin(β)), v, 0, 1, β, 0, α], k, 0, m - 1) → Inners
31. Sequence(Surface[2 - ((2 - ((k + u) * h)) * cos(β)), g(((k + p) * h)), ((2 - ((k + u) * h)) * sin(β)), u, 0, 1, β, 0, α], k, 0, m - 1) → Fronts
32. Sequence(Surface[2 - ((2 - ((k + u) * h)) * cos(β)), f(((k + p) * h)), ((2 - ((k + u) * h)) * sin(β)), u, 0, 1, β, 0, α], k, 0, m - 1) → Backs
33. RectangleSum((((2 * π) * R(x)) * H(x)), 0, (m * h), m, p) → VolShells