# Integral x(t) (G Dataflow)

Last Modified: July 17, 2019

Performs the discrete integration of the sampled signal.  ## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number to x(t).

Default: False ## x(t)

Sampled signal from time 0 to n-1, where n is the number of elements in the sampled signal.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers. ## integration method

Method to use to perform the numeric integration.

Name Value Description
Trapezoidal Rule 0 Uses the trapezoidal rule defined by the following equation:

Let x(t) be a function of t and t1 - t0 = dt, then

${\int }_{{t}_{0}}^{{t}_{1}}x\left(t\right)dt\approx \frac{dt}{2}\left(x\left({t}_{0}\right)+x\left({t}_{1}\right)\right)$
Simpson's Rule 1 Uses the Simpson's rule defined by the following equation:

Let x(t) be a function of t and t1 - t0 = t2 - t1 = dt, then

${\int }_{{t}_{0}}^{{t}_{2}}x\left(t\right)dt\approx \frac{dt}{3}\left(x\left({t}_{0}\right)+4x\left({t}_{1}\right)+x\left({t}_{2}\right)\right)$
Simpson's 3/8 Rule 2 Uses the Simpson's 3/8 rule defined by the following equation:

Let x(t) be a function of t and t1 - t0 = t2 - t1 = t3 - t2 = dt, then

${\int }_{{t}_{0}}^{{t}_{3}}x\left(t\right)dt\approx \frac{3dt}{8}\left(x\left({t}_{0}\right)+3x\left({t}_{1}\right)+3x\left({t}_{2}\right)+x\left({t}_{3}\right)\right)$
Boole's Rule 3 Uses the Boole's rule defined by the following equation:

Let x(t) be a function of t and t1 - t0 = t2 - t1 = t3 - t2 = t4 - t3 = dt, then

${\int }_{{t}_{0}}^{{t}_{4}}x\left(t\right)dt\approx \frac{2dt}{45}\left(7x\left({t}_{0}\right)+32x\left({t}_{1}\right)+12x\left({t}_{2}\right)+32x\left({t}_{3}\right)+7x\left({t}_{4}\right)\right)$
Forward Euler 4 Uses the forward Euler rule defined by the following equation:

Let x(t) be a function of t and t 1 - t 0 = dt, then

${\int }_{{t}_{0}}^{{t}_{1}}x\left(t\right)dt\approx dt\cdot x\left({t}_{0}\right)$
Backward Euler 5 Uses the backward Euler rule defined by the following equation:

Let x(t) be a function of t and t 1 - t 0 = dt, then

${\int }_{{t}_{0}}^{{t}_{1}}x\left(t\right)dt\approx dt\cdot x\left({t}_{1}\right)$

Default: Simpson's Rule ## 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 ## dt

Sampling interval.

Default: 1 ## integral x(t)

Discrete integration of the sampled signal.

This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers. ## 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.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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