2Lapp_Oberfläche_Riemannsumme_20erTeilung_mitWurzel

Intervall dx

b

\Delta b

\sqrt{1-x^2}

\Delta A = \sqrt{1-x^2} \cdot \Delta b

A = \int_{0}^{1}{\sqrt{1-x^2} \cdot \sqrt{1+16x^2}\, dx}

g(x, y) = If[sqrt(x^(2) + y^(2)) ≤ 1, 0]
c = Surface(cos(t), sin(t), ((h * 2) * (cos(t))^(2)), t, 0, (2 * pi), h, 0, 1)
d(x, y) = If[sqrt(x^(2) + y^(2)) ≤ 1, (1 / 2 * (x + y - ((-x) + y))^(2))]
a = CurveCartesian(cos(t), sin(t), (2 * (cos(t))^(2)), t, 0, (2 * pi))
b = CurveCartesian(t, 0, (2 * t^(2)), t, -1, 1)
x_{P} = 0.1 (slider from 0 to 1, step 0.05)
P: (x_{P}, 0, (-2 * x_{P}^(2)))
Q: (x_{P}, sqrt(1 - x_{P}^(2)), (-2 * x_{P}^(2)))
f = Segment(P, Q)
d_{x}: 0.972
e = Length(b, 0, d_{x})
h = Length(b, 0, 1)
B2: h
A3: 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
A11: A10 + 1
A12: A11 + 1
B3_{1}: (B2 / 10 * A3)
B3_{2}: (A3 * $B$2 / 10)
D4: 0
D5: 0
D6: 0
D7: 0
D8: 0
D9: 0
D10: 0
D11: 0
D12: 0
B3: (A3 * $B$2 / 20)
B4: (A4 * $B$2 / 20)
B5: (A5 * $B$2 / 20)
B6: (A6 * $B$2 / 20)
B7: (A7 * $B$2 / 20)
B8: (A8 * $B$2 / 20)
B9: (A9 * $B$2 / 20)
B10: (A10 * $B$2 / 20)
B11: (A11 * $B$2 / 20)
B12: (A12 * $B$2 / 20)
A13: A12 + 1
A14: A13 + 1
A15: A14 + 1
A16: A15 + 1
A17: A16 + 1
A18: A17 + 1
A19: A18 + 1
A20: A19 + 1
A21: A20 + 1
A22: A21 + 1
B13: (A13 * $B$2 / 20)
B14: (A14 * $B$2 / 20)
B15: (A15 * $B$2 / 20)
B16: (A16 * $B$2 / 20)
B17: (A17 * $B$2 / 20)
B18: (A18 * $B$2 / 20)
B19: (A19 * $B$2 / 20)
B20: (A20 * $B$2 / 20)
B21: (A21 * $B$2 / 20)
B22: (A22 * $B$2 / 20)
C22: 1
C20: 0.942000000000001
C18: 0.881
C16: 0.815000000000001
C14: 0.744000000000001
C12: 0.666000000000001
C10: 0.580000000000001
C8: 0.481
C6: 0.362
C4: 0.21
C3: 0.113
C5: 0.292
C7: 0.425
C9: 0.532
C11: 0.624
C13: 0.706
C15: 0.78
C17: 0.848
C19: 0.911
C21: 0.971
D13: 0
D14: 0
D15: 0
D16: 0
D17: 0
D18: 0
D19: 0
D20: 0
D21: 0
D22: 0
E3: (2 * C3^(2))
E4: (2 * C4^(2))
E5: (2 * C5^(2))
E6: (2 * C6^(2))
E7: (2 * C7^(2))
E8: (2 * C8^(2))
E9: (2 * C9^(2))
E10: (2 * C10^(2))
E11: (2 * C11^(2))
E12: (2 * C12^(2))
E13: (2 * C13^(2))
E14: (2 * C14^(2))
E15: (2 * C15^(2))
E16: (2 * C16^(2))
E17: (2 * C17^(2))
E18: (2 * C18^(2))
E19: (2 * C19^(2))
E20: (2 * C20^(2))
E21: (2 * C21^(2))
E22: (2 * C22^(2))
B: (C4, D4, E4)
C: (C5, D5, E5)
D: (C6, D6, E6)
E: (C7, D7, E7)
F: (C8, D8, E8)
G: (C9, D9, E9)
H: (C10, D10, E10)
I: (C11, D11, E11)
J: (C12, D12, E12)
K: (C13, D13, E13)
L: (C14, D14, E14)
M: (C15, D15, E15)
N: (C16, D16, E16)
O: (C17, D17, E17)
R: (C18, D18, E18)
S: (C19, D19, E19)
T: (C20, D20, E20)
U: (C21, D21, E21)
V: (C22, D22, E22)
D3: 0
A: (C3, D3, E3)
l1: {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, R, S, T, U, V}
C25: 0.113
E25: 0.025538
C26: 0.21
E26: 0.0882000000000001
C27: 0.292
E27: 0.170528
C28: 0.362
E28: 0.262088
C29: 0.425
E29: 0.36125
C30: 0.481000000000001
E30: 0.462722
C31: 0.532000000000001
E31: 0.566048000000001
C32: 0.580000000000002
E32: 0.672800000000003
C33: 0.624000000000001
E33: 0.778752000000001
C34: 0.666000000000002
E34: 0.887112000000004
C35: 0.706000000000001
E35: 0.996872000000001
C36: 0.744000000000002
E36: 1.107072
C37: 0.780000000000001
E37: 1.2168
C38: 0.815000000000002
E38: 1.32845
C39: 0.848000000000001
E39: 1.438208
C40: 0.881000000000001
E40: 1.552322
C41: 0.911000000000001
E41: 1.659842
C42: 0.942000000000002
E42: 1.77472800000001
C43: 0.971000000000001
E43: 1.885682
C44: 1
E44: 2
D25: sqrt(1 - C25^(2))
D26: sqrt(1 - C26^(2))
D27: sqrt(1 - C27^(2))
D28: sqrt(1 - C28^(2))
D29: sqrt(1 - C29^(2))
D30: sqrt(1 - C30^(2))
D31: sqrt(1 - C31^(2))
D32: sqrt(1 - C32^(2))
D33: sqrt(1 - C33^(2))
D34: sqrt(1 - C34^(2))
D35: sqrt(1 - C35^(2))
D36: sqrt(1 - C36^(2))
D37: sqrt(1 - C37^(2))
D38: sqrt(1 - C38^(2))
D39: sqrt(1 - C39^(2))
D40: sqrt(1 - C40^(2))
D41: sqrt(1 - C41^(2))
D42: sqrt(1 - C42^(2))
D43: sqrt(1 - C43^(2))
D44: sqrt(1 - C44^(2))
A_1: (C25, D25, E25)
B_1: (C26, D26, E26)
C_1: (C27, D27, E27)
D_1: (C28, D28, E28)
E_1: (C29, D29, E29)
F_1: (C30, D30, E30)
G_1: (C31, D31, E31)
H_1: (C32, D32, E32)
I_1: (C33, D33, E33)
J_1: (C34, D34, E34)
K_1: (C35, D35, E35)
L_1: (C36, D36, E36)
M_1: (C37, D37, E37)
N_1: (C38, D38, E38)
O_1: (C39, D39, E39)
P_1: (C40, D40, E40)
Q_1: (C41, D41, E41)
R_1: (C42, D42, E42)
S_1: (C43, D43, E43)
v1, a_1, i, b_1, b_2 = Polygon(A, A_1, B_1, B)
v2, b_3, j, c_1, c_2 = Polygon(B, B_1, C_1, C)
v3, c_3, k, d_1, d_2 = Polygon(C, C_1, D_1, D)
v4, d_3, l, e_1, e_2 = Polygon(D, D_1, E_1, E)
v5, e_3, m, n, f_2 = Polygon(E, E_1, F_1, F)
v6, f_3, p, g_1, g_2 = Polygon(F, F_1, G_1, G)
v7, g_3, q, h_1, h_2 = Polygon(G, G_1, H_1, H)
v8, h_3, r, i_1, i_2 = Polygon(H, H_1, I_1, I)
v9, i_3, s, j_1, j_2 = Polygon(I, I_1, J_1, J)
v10, j_3, t, k_1, k_2 = Polygon(J, J_1, K_1, K)
v11, k_3, l_1, m_1, l_2 = Polygon(K, K_1, L_1, L)
v12, l_3, n_1, p_1, m_2 = Polygon(L, L_1, M_1, M)
v13, m_3, q_1, r_1, n_2 = Polygon(M, M_1, N_1, N)
v14, n_3, s_1, o_1, o = Polygon(N, N_1, O_1, O)
v15, o_2, t_1, p_2, r_2 = Polygon(O, O_1, P_1, R)
v16, r_3, q_2, s_2, s_3 = Polygon(R, P_1, Q_1, S)
v17, s_4, t_2, a_2, t_3 = Polygon(S, Q_1, R_1, T)
v18, t_4, p_3, q_3, u = Polygon(T, R_1, S_1, U)
Z_1: (0, 1, 0)
Z_0: (0, 0, 0)
v19, z_0, z_1, f_1, a_3 = Polygon(Z_0, Z_1, A_1, A)
d1, v, u_1, f_4 = Polygon(U, S_1, V)
w = CurveCartesian(cos(t), sin(t), 0, t, 0, (2 * pi))
W = Point(k_3)
Z = (0.9454124839250344, 0.7407644118548662, 1)
g_4 = Segment(W, Z)
K_2: (C35, D35, 0)
h_4 = Segment(K_1, K_2)
i_4 = Segment((0, 0, 0), K_2)
K_3: (C35, 0, 0)
j_4 = Segment(K_2, K_3)
k_4 = Segment(K, K_3)