G_s(t)

g_s(t)=g(t)\cdot e^{-s\;t}\
g_s(t)=\cos{t}\cdot e^{\frac{1}{5}t-s\;t}\

G_s(t)=\int g_s(t){\rm d}t

G_s=(s,G_s(0))

G(s)=\int_0^∞g_s(t,s){\rm d}t

Zwischenschritte

Bildbereich

-G_s(0)

s = 0.6 (slider from -1 to 10, step 0.1)
G(t) = (((5 * exp(((-((-(1 / 5)) + s)) * t))) * (cos(t) - ((5 * s) * cos(t)) + (5 * sin(t))))) / (26 - (10 * s) + (25 * s^(2)))
g_s(t) = (exp(t / 5 - (s * t)) * cos(t))
S: (s, 0)
G_s: (s, G(0))
B: (0, G(0))
O: (0, 0)
g = OrthogonalLine(B, yAxis)
h = OrthogonalLine(G_s, yAxis)
Gvons = Locus(G_s, s)
i = Segment(O, B)
j = Segment(O, S)
k = Segment(S, G_s)
u = Vector(S, G_s)
A = (10.12791140905832, 0.7296052429855743)
C = (11.844618455343985, 0.7296052429855743)
D = (10.128582892072396, 0.9971705889673489)
Wert = Integral(g_s, 0, 12)
E = Mirror(G_s, xAxis)
Ortslinie1 = Locus(E, s)
v = Vector(S, E)
Text7: "|\overrightarrow{OB}|=" + (LaTeX[i]) + ""