# Integration (G Dataflow)

Calculates both function values and integral values of a given function of one variable.

## number of points

Number of values of the independent variable used in the function calculation.

Default: 10

## formula

Formula that defines the function. The formula can contain any number of valid variables.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores.

## start

Start value of the interval where this node starts calculating values.

Default: 0

## end

End value of the interval where this node stops calculating values.

Default: 1

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## x values

Variable values used in the function calculation. The values are equally spaced from start to end.

## y values

Function values at the corresponding points in x values.

## integral of y

Integral values of formula between start and end at x values.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating integral of y

The node calculates integral of y of a given function f(t) between start and end using the following equation:

$I=\underset{\mathrm{start}}{\overset{\mathrm{end}}{\int }}f\left(t\right)dt$

You can reformulate the previous equation to the following ordinary differential equation, which is solved using the Runge Kutta method.

$\left\{\begin{array}{c}\frac{dI\left(s\right)}{ds}=f\left(s\right)\\ I\left(\mathrm{start}\right)=0\end{array}$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application