' arcSin improper integral numerically: Simpson's rule of numerical calculation of integral
n = 15107096
k = n Mod 10000
T = n Mod 100
Dim f(9999999)
'
pi = 4 * Atn(1)
'
a = 0
b = 1
nn = 9999998
h = (b - a) / nn
'
For k = 0 To nn - 1
x = a + k * (b - a) / nn
v = 1 / Sqr(1 - x ^ 2)
f(k) = v
Next k
'
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
'
ArcSin_improper_integral_numerically = (f(0) + 2 * i2j + 4 * i2jm1 + f(nn)) * h / 3
'
MsgBox ArcSin_improper_integral_numerically
d1 = Abs(i - 1 / 5)
'MsgBox d1
d2 = Abs(4 * 3 * 2 * 1 / (180 * nn ^ 4))
'MsgBox d2
dd = Abs(d1 - d2)
'MsgBox dd