2009年AB微积分第4c题：方形截面体积

GeoGebra 命令及参数

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