2015年AP微积分考试2b题体积计算

GeoGebra 命令及参数

1. Intersect(f, g, (1.0328318883641743, 2.401108092689728)) → L
2. Polygon(B, A, C, D) → Square, c, d, e, i
3. Segment(A, B) → b
4. Locus(D, s) → loc1
5. Integral(ht(x)^(2), a, 2) → Integ
6. If(togDF ≟ 1, "Show Instructions", "Show volume integral") → ToggleDirectionVolumeIntegral
7. Locus(C, s) → loc2
8. Angle(B, A, C) → α
9. If(togS ≟ 0, "Show Surface", "Hide Surface") → ShowSurface
10. Surface(u, f(u), (v * (f(u) - g(u))), u, xl, 2, v, 0, 1) → Back
11. Surface(u, (v * g(u)) + ((1 - v) * f(u)), 0, u, xl, 2, v, 0, 1) → Base
12. Surface(u, g(u), (v * (f(u) - g(u))), u, xl, 2, v, 0, 1) → Front
13. Surface(u, (v * g(u)) + ((1 - v) * f(u)), f(u) - g(u), u, xl, 2, v, 0, 1) → Top
14. Sequence(Polygon[(a + (k * h), g(a + ((k + p) * h)), 0), (a + (k * h), f(a + ((k + p) * h)), 0), (a + (k * h), f(a + ((k + p) * h)), ht(a + ((k + p) * h))), (a + (k * h), g(a + ((k + p) * h)), ht(a + ((k + p) * h)))], k, 0, m - 1) → SlicesLeft
15. Sequence(Area[Element[SlicesLeft, k]], k, 1, m) → Areas
16. Sequence(Surface[a + u, f(a + ((k + p) * h)), (v * ht(a + ((k + p) * h))), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesBack
17. Sequence(Polygon[(a + (k * h), g(a + ((k + p) * h))), (a + ((k + 1) * h), g(a + ((k + p) * h))), (a + ((k + 1) * h), f(a + ((k + p) * h))), (a + (k * h), f(a + ((k + p) * h)))], k, 0, m - 1) → SlicesBase
18. Sequence(Surface[a + u, g(a + ((k + p) * h)), (v * ht(a + ((k + p) * h))), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesFront
19. Sequence(Polygon[(a + ((k + 1) * h), g(a + ((k + p) * h)), 0), (a + ((k + 1) * h), f(a + ((k + p) * h)), 0), (a + ((k + 1) * h), f(a + ((k + p) * h)), ht(a + ((k + p) * h))), (a + ((k + 1) * h), g(a + ((k + p) * h)), ht(a + ((k + p) * h)))], k, 0, m - 1) → SlicesRight
20. Sequence(Surface[a + u, (v * g(a + ((k + p) * h))) + ((1 - v) * f(a + ((k + p) * h))), ht(a + ((k + p) * h)), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesTop