' Simpson's rule of numerical calculation of integral
n = 15107096
k = n Mod 10000
T = n Mod 100
Dim f(99)
a = 1 / n
b = 1 / k
n = 88
h = (b - a) / n
'
For k = 0 To n
x = a + k * (b - a) / n
v = 1 + Cos(T * x)
f(k) = v
Next k
'
i2j = 0
For j = 1 To n / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To n / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
i = (f(0) + 2 * i2j + 4 * i2jm1 + f(n)) * h / 3
'
'MsgBox i
average_value_of_conntinuous_function = i / (b - a)
MsgBox average_value_of_conntinuous_function
d1 = Abs(i - 1 / 5)
'MsgBox d1
d2 = Abs(4 * 3 * 2 * 1 / (180 * n ^ 4))
'MsgBox d2
dd = Abs(d1 - d2)
'MsgBox dd