The x values you wire to this VI must be evenly spaced, or result is incorrect. If the values are not evenly spaced, you can use the Uneven Numeric Integration VI to compute the integral.

1D Numeric Integration

If 224 points are provided and the Bode Method is chosen, the VI arrives at the result by performing 55 Bode Method partial evaluations and one Simpsons' 3/8 Method evaluation.

Each of the methods depends on the sampling interval (dt) and computes the integral using successive applications of a basic formula in order to perform partial evaluations, which depend on some number of adjacent points. The number of points used in each partial evaluation represents the order of the method. The result is the summation of these successive partial evaluations.

where j is a range dependent on the number of points and the method of integration.

The following are the basic formulas for the computation of the partial sum of each rule in ascending method order:

• Trapezoidal: 1/2(x[i] + x[i + 1])*dt
• Simpsons': (x[2i] + 4x[2i + 1] + x[2i + 2])*dt/3, k = 2
• Simpsons' 3/8: (3x[3i] + 9x[3i + 1] + 9x[3i + 2] + 3x[3i + 3]) * dt/8, k = 3

• Bode: (14x[4i] + 64x[4i + 1] + 24x[4i + 2] + 64x[4i + 3] + 14x[4i + 4]) * dt/45, k = 4

  for i = 0, 1, 2, 3, 4, ..., Integral Part of [(N – 1)/k]

where N is the number of data points, k is an integer dependent on the method, and x is the input array.

2D Numeric Integration

To perform the 2D numeric integration of

,

this VI first applies 1D numeric integration over x to evaluate

.

Then this VI applies 1D numeric integration over y to obtain the result

3D Numeric Integration

To perform the 3D numeric integration of

,

this VI applies 1D numeric integration over x, y, and z, in sequence, as shown by the following equations: