' x and y coordinates of curves center of mass: Simpson's rule of numerical calculation of integral
n = 15107096
k = n Mod 10000
T = n Mod 100
Dim f(999)
'
pi = 4 * Atn(1)
'
a = 1 / n
b = 1 / k
nn = 88
h = (b - a) / nn
'
For kk = 0 To nn
x = a + kk * (b - a) / nn
f(kk) = x * Sqr(1 + (T * Sin(T * x)) ^ 2)
Next kk
'
i2j = 0
For j = 1 To nn / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To nn / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
x_times_length_integral = (f(0) + 2 * i2j + 4 * i2jm1 + f(nn)) * h / 3
'
'
For kk = 0 To nn
x = a + kk * (b - a) / nn
f(kk) = Sqr(1 + (T * Sin(T * x)) ^ 2)
Next kk
'
i2j = 0
For j = 1 To nn / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To nn / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
arc = (f(0) + 2 * i2j + 4 * i2jm1 + f(nn)) * h / 3

x_curves_center_of_mass = x_times_length_integral / arc
'
y_curves_center_of_mass = 1 + Cos(T * x_curves_center_of_mass)
ya = 1 + Cos(T * a)
yb = 1 + Cos(T * b)
'MsgBox a
MsgBox x_curves_center_of_mass
'MsgBox b
'MsgBox ya
MsgBox y_curves_center_of_mass
'MsgBox yb