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2009年B卷第4题：AB2009_4b_B

2009年B卷第4题：AB2009_4b_B
几何画板及绘图内容加载中，请稍等……
2016-03-19 11:23
立体几何微积分积分
所属专题 AP Calculus volume problems
该范例演示了2009年AP考试B卷第4题，涉及立体几何中的体积计算。通过使用GeoGebra命令如Intersect、Segment、Integral等，可以动态展示底面为正方形的立体图形。该范例适合高中数学教学，特别是微积分和立体几何的学习。

GeoGebra 命令及参数

  1. Intersect(f, g, 3, 5) → E
  2. Segment(A, B) → e
  3. Integral((g(x) - f(x))^(2), 0, 4) → Integ
  4. Locus(C, s) → loc1
  5. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
  6. Locus(D, s) → loc2
  7. Polygon(A, B, C, D) → Rect, a, b, c, d
  8. Angle(B, A, D) → α
  9. Segment((0, 6, 27), (9, 6, 27)) → i
  10. Surface(u, (v * f(u)) + ((1 - v) * g(u)), 0, u, 0, 4, v, 0, 1) → Base
  11. Surface(u, (v * f(u)) + ((1 - v) * g(u)), g(u) - f(u), u, 0, 4, v, 0, 1) → Top
  12. Surface(u, f(u), (v * (g(u) - f(u))), u, 0, 4, v, 0, 1) → SurfaceRight
  13. Surface(u, g(u), (v * (g(u) - f(u))), u, 0, 4, v, 0, 1) → SurfaceLeft
  14. If(togDF ≟ 1, "Show Directions", "Show volume integral") → ToggleDirectionVolumeIntegral
  15. Sequence(Polygon[((k * h), f(((k + p) * h)), 0), ((k * h), g(((k + p) * h)), 0), ((k * h), g(((k + p) * h)), ht(((k + p) * h))), ((k * h), f(((k + p) * h)), ht(((k + p) * h)))], k, 0, m - 1) → SlicesLeft
  16. Sequence(Polygon[(((k + 1) * h), f(((k + p) * h)), 0), (((k + 1) * h), g(((k + p) * h)), 0), (((k + 1) * h), g(((k + p) * h)), ht(((k + p) * h))), (((k + 1) * h), f(((k + p) * h)), ht(((k + p) * h)))], k, 0, m - 1) → SlicesRight
  17. Sequence(Surface[((k + u) * h), (v * f(((k + p) * h))) + ((1 - v) * g(((k + p) * h))), ht(((k + p) * h)), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesTop
  18. Sequence(Surface[((k + u) * h), f(((k + p) * h)), (v * ht(((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesFront
  19. Sequence(Surface[((k + u) * h), g(((k + p) * h)), (v * ht(((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesBack
  20. Sequence(Polygon[((k * h), f(((k + p) * h)), 0), ((k * h), g(((k + p) * h)), 0), (((k + 1) * h), g(((k + p) * h)), 0), (((k + 1) * h), f(((k + p) * h)), 0)], k, 0, m - 1) → SlicesBase
  21. Sequence(Area[Element[SlicesLeft, k]], k, 1, m) → Areas