旋转体的体积：盘旋法

GeoGebra 命令及参数

1. Textfield(f) → Function
2. Textfield(a) → Textfeld2
3. Textfield(b) → Textfeld3
4. CurveCartesian(t, (f(t) * cos(φ)), (f(t) * sin(φ)), t, a, b) → k_x
5. Ray((0, c), Vector[(1, 0)]) → g_1
6. Intersect(f, g_1, (1, f(1))) → I
7. Ray((0, d), Vector[(1, 0)]) → g_2
8. Intersect(f, g_2, (d, f(d))) → J
9. CurveCartesian((t * cos(ϕ)), f(t), (t * sin(ϕ)), t, x(I), x(J)) → k_y
10. CurveCartesian(t, f(t), 0, t, -5, 5) → k
11. Textfield(c) → Textfeld4
12. Textfield(d) → Textfeld5
13. Segment(A, G) → s_1
14. Segment(B, F) → s_2
15. Surface(u, (f(u) * cos(w)), (f(u) * sin(w)), u, a, b, w, 0, φ) → f_x
16. Surface((uu * cos(ww)), f(uu), (uu * sin(ww)), uu, x(I), x(J), ww, 0, ϕ) → f_y
17. Invert(f) → f_u
18. Segment(C, I) → s_3
19. Segment(D, J) → s_4
20. CurveCartesian(x(B), t, t, y(B), f(x(B))) → LineCapRight
21. CurveCartesian(x(A), t, t, y(A), f(x(A))) → LineCapLeft
22. Surface(x(A), y(A) + ((s * (f(x(A)) - y(A))) * cos(t)), ((s * (f(x(A)) - y(A))) * sin(t)), s, 0, 1, t, 0, φ) → CapLeft
23. Surface(x(B), y(B) + ((s * (f(x(B)) - y(B))) * cos(t)), ((s * (f(x(B)) - y(B))) * sin(t)), s, 0, 1, t, 0, φ) → CapRight
24. CurveCartesian(t, y(C), t, x(C), f_u(y(C))) → LineCapBottom
25. CurveCartesian(t, y(D), t, x(D), f_u(y(D))) → LineCapTop