圆柱与正弦波面积计算

GeoGebra 命令及参数

1. If(theta ≤ π / 2, π / 2, If[theta ≥ (3 * π / 2), (3 * π / 2), theta]) → theta_{cond}
2. Segment(A, B) → i
3. Plane(PlaneRef, PlaneRef2, PlaneRef2 + (0, 1, 0)) → p
4. Segment(A_{2D}, B_{2D}) → g
5. Integral(IntFun, 0, theta) → Area_{Peel}
6. Text("Area of Peel: " + Area_{Peel}) → text1
7. Integral(IntFun_{Sliced}, π / 2, theta_{cond}) → Area_{SlicedPeel}
8. Segment(A_{2DSliced}, B_{2DSliced}) → j
9. Text("Area of Sliced Peel: " + Area_{SlicedPeel}) → text2
10. Cylinder((0, 0, (-(R / 2))), (0, 0, R / 2), R) → C, C_{2}, C_{3}, C_{4}
11. Segment(A, B + (0, 0, R / 2)) → h
12. Circle(O, R, Vector[(0, 0, 0), (0, 0, 1)]) → c
13. Polygon(O, E, A) → t1, a, o, e
14. Segment((0, (-R), 0), (0, R, 0)) → k
15. Polygon(O, E, F) → t2, f_1, o_1, e_1
16. Text("R*Sin(θ - π/2)*tan(α)", Midpoint[o]) → text3
17. Text("R*Sin(θ - π/2)", Midpoint[o_1]) → text4
18. Text("y = R*(1+Sin(x - π/2))*tan(α)") → text5
19. Angle(E, O, (1, 0, (-(R / 2)))) → θ
20. CircleSector(O, (R / 4, 0, (-(R / 2))), (R / 4; θ; 0) - (0, 0, R / 2), xOyPlane) → θ_{sector}
21. Segment(A, F) → l
22. Angle(A, F, B) → Alpha