numerical integration

[thinktank2]

òdq / Ö(1- k.Sin(q)²)

For k = 1,

This function doesn't seem to converge between the limits specified. But it does for 0 to Pi/4. There will be a divide by zero error for 0 to Pi/2. Since Sin(Pi/2) = 1, the denominator becomes 0.

Private Sub Form_Load()
Dim Pi As Double
Pi = 4 * Atn(1)
 
'MsgBox Simpson(Pi / 2, 0, 100)  ---> Error
 
 MsgBox Simpson(Pi/4, 0, 100)  '--> works
 
End Sub
 
'------ > Function Definition
Private Function F(x As Double) As Double
F = 1 / Sqr(1 - (Sin(x) ^ 2))
End Function
 
Private Function Simpson(U As Double, L As Double, N As Double) As Double
'U  Upper Limit
'L  Lower Limit
'N  Number of Intervals
'H  Interval
 
H = (U - L) / N
 
Total = F(L)
 
For i = 1 To (N / 2) - 1
    Total = Total + 4 * F(L + ((2 * i) - 1) * H) + 2 * F(L + (2 * i * H))
Next
 
Total = Total + F(U)
 
Simpson = (H / 3) * Total
 
End Function