h

a

g(x)= \lambda f(x)

\int_a^b \lambda f=\lambda\int_a^b f

f

b

b

Zwischenflächen sind
unabhängig von der Höhenlage

t_1 = -0.5
g_{1}(x) = (t_1 * (x - 1.5)^(2)) + 1.2
a_4 = 3.5
a_3 = 4
a_2: 1
a_1: 0.5
t = 0.2
h(x) = ((((t * (x - a_1)) * (x - a_4)) * (x - a_2)) * (x - a_3)) + 0.4
hz(x) = h(x) - 0.8
lam = 3 (slider from -5 to 5, step 0.5)
ss = 1 (slider from -5 to 5, step 0.6)
g(x) = (lam * h(x))
T, U = Intersect(g_{1}, hz)
a: x(T)
A: (a, 0)
ep: 0.25
S: (ss, h(ss))
s: x(S)
S': (s + ep, g_{1}(s + ep))
S_u: (s, 0)
S'_u: (s + ep, 0)
S_h: (s, h(s))
S'_h: (s + ep, h(s + ep))
S_f: (s, g(s))
S'_f: (s + ep, g(s + ep))
v4, s_1, s', s'_f, s_f = Polygon(S, S', S'_f, S_f)
v5, s_2, i, s'_u, s_u = Polygon(S, S', S'_u, S_u)
v6, n, s_h, s'_h, p = Polygon(S_u, S_h, S'_h, S'_u)
c: 1
j = Segment(S_f, S_u)
C = Midpoint(S_f, S)
k = Segment(S, S_u)
l = Segment(S_f, C)
m = Segment(C, S)
b: x(U)
gh(x) = g_{1}(x) + 2
hzh(x) = hz(x) + 2
B: (b, 0)
D = Point(xAxis)
Int_{ab} = Integral(g, a, x(D))
Int_h = Integral(h, a, x(D))
Int_z = IntegralBetween(g_{1}, hz, a, b)
Int_o = IntegralBetween(gh, hzh, a, b)
Text6: "Grün = " + lam + " mal Kariert"
E = (5.772870567223871, 0.16421832462551555)
F = (6.599537233890537, 0.16421832462551555)
Text4: "" + (LaTeX[lam]) + " f"