Numeric Integration (Not in Base Package)

Performs a numeric integration on the input array of data using one of four popular numeric integration methods. Details

Input Array contains the data to be integrated, which is obtained from sampling some function f(t) at multiples of dt, that is, f(0), f(dt), f(2dt),…
dt is the interval size, which represents the sampling step size used in obtaining data in Input Array from the function. If you supply a negative dt, the VI uses its absolute value.
integration method specifies the method used in performing the numeric integration.

0Trapezoidal Rule
1Simpsons' Rule
2Simpsons' 3/8 Rule
3Bode Rule
result contains the result of the numeric integration.
error returns any error or warning condition from the VI.

Numeric Integration Details

Number of PointsPartial Evaluations Performed
22455 Bode, 1 Simpsons’ 3/8
22556 Bode
22656 Bode, Trapezoidal
22756 Bode, 1 Simpsons'
22857 Bode, 1 Simpsons’ 3/8

If 224 points were provided and the Bode Method was chosen, the VI would arrive at the result by performing 55 Bode Method partial evaluations and one Simpsons' 3/8 Method evaluation.

Each of the methods depend on the sampling interval (dt) and compute 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:

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

Note  If the number of points provided for a certain chosen method does not contain an integral number of partial sums, then the method is applied for all possible points. For the remaining points, the next possible lower order method is used. For example, if the Bode method is selected, the previous example shows what this VI evaluates for different numbers of points.