t_1

t_2

\varrho(t) = \frac{1}{T}

\textrm{Zeit }t\,\,\,\textrm{(s)}

\textrm{Fallstrecke }x \,\,\, \textrm{(m)}

h

x_1

x_2

\varrho(x) = \frac{1}{2\sqrt{hx}}

T

x_1 = \frac{g}{2}t_1^2\quad\textrm{und}\quad x_2 = \frac{g}{2}t_2^2

F = Point(xAxis)
T: x(F)
g: 9.81
h: (g / 2 * T^(2))
tdichte: 1 / T
rho(x) = If[0 ≤ x ≤ h, 1 / ((2 * sqrt((h * x))))]
rhot(x) = If[0 ≤ x ≤ T, tdichte + (0 * x)]
A = Point(xAxis)
B = Point(xAxis)
t_1: x(A)
t_2: x(B)
pt = Integral(rhot, t_1, t_2)
x_1: (g / 2 * t_1^(2))
x_2: (g / 2 * t_2^(2))
C: (x_1, 0)
D: (x_2, 0)
px = Integral(rho, x_1, x_2)
E: (h, 0)
Text11: "\int_{t_1}^{t_2}\varrho(t)\,\textrm{d}t = " + (LaTeX[pt]) + ""
Text12: "\int_{x_1}^{x_2}\varrho(x)\,\textrm{d}x = " + (LaTeX[px]) + ""