u=u(x)

x=f(u)

x=f(u)

f'(u)

h(u)=g(f(u))

\int_a^b{g(x)\ {\rm d}x}=★

★=\int_a^b{h(u)f'(u)}\;{\rm d}u

Spiegelung verbergen

Bewege A bis G mit den 
Pfeiltasten auf oder ab,
um die Transformation
u=u(x) festzulegen.

n = 6 (slider from 2 to 20, step 1)
a: 1
b: 4
δ: (b - a) / n
l2 = Sequence(x = a + (i * δ), i, 0, n, 1)
A = Point(l2)
B = Point(l2)
C = Point(l2)
D = Point(l2)
E = Point(l2)
F = Point(l2)
G = Point(l2)
w: y = x
A' = Mirror(A, w)
B' = Mirror(B, w)
C' = Mirror(C, w)
D' = Mirror(D, w)
E' = Mirror(E, w)
F' = Mirror(F, w)
G' = Mirror(G, w)
f = Polynomial({A', B', C', D', E', F', G'})
f'(x) = f'(x)
g(x) = 2 - x^(2) / 8
fp(x) = If[x ≥ x(A') ∧ x ≤ x(G'), f(x)]
u = Mirror(fp, w)
l1 = Sequence((a + (i * δ), 0), i, 0, n, 1)
H = Point(l1)
h(x) = g(f(x))
I = Point(xAxis)
i_{2} = Segment(B, I)
J = Point(xAxis)
j = Segment(C, J)
K = Point(l1)
k = Segment(D, K)
L = Point(xAxis)
l = Segment(E, L)
M = Point(l1)
m = Segment(F, M)
N = Point(g)
p = Segment(G, N)
q = OrthogonalLine(A, yAxis)
r = OrthogonalLine(B, yAxis)
s = OrthogonalLine(C, yAxis)
t = OrthogonalLine(D, yAxis)
c = OrthogonalLine(E, yAxis)
d = OrthogonalLine(F, yAxis)
e = OrthogonalLine(G, yAxis)
O = Intersect(e, q)
P = Intersect(q, yAxis)
Q = Intersect(r, yAxis)
R = Intersect(s, yAxis)
S = Intersect(t, yAxis)
T = Intersect(c, yAxis)
U = Intersect(d, yAxis)
V = Intersect(e, yAxis)
f_1 = Segment(P, A)
g_1 = Segment(Q, B)
h_1 = Segment(B, Q)
i_1 = Segment(R, C)
j_1 = Segment(S, D)
k_1 = Segment(T, E)
l_1 = Segment(U, F)
m_1 = Segment(V, G)
i(x) = (h(x) * f'(x))
o = TrapezoidalSum(g, a, b, n)
int_{h f'} = Integral(i, x(A'), x(G'))
int_g = Integral(g, a, b)
P' = Mirror(P, w)
Q' = Mirror(Q, w)
R' = Mirror(R, w)
S' = Mirror(S, w)
T' = Mirror(T, w)
U' = Mirror(U, w)
V' = Mirror(V, w)
n_1 = OrthogonalLine(P', xAxis)
q_1 = OrthogonalLine(V', xAxis)
P'' = Intersect(i, n_1)
v = false
A'': A'
B'': B'
C'': C'
D'': D'
E'': E'
F'': F'
G'': G'
Z = Point(Circle[P', i(x(P'))])
r_1 = Segment(P', (x(P'), i(x(P'))))
s_1 = Segment(Q', (x(Q'), i(x(Q'))))
p_1 = Segment(R', (x(R'), i(x(R'))))
t_1 = Segment(S', (x(S'), i(x(S'))))
c_1 = Segment(T', (x(T'), i(x(T'))))
d_1 = Segment(U', (x(U'), i(x(U'))))
e_1 = Segment(V', (x(V'), i(x(V'))))
a_1 = Segment(A, H)