# 2.8.8 Integ1

Analysis: Mathematics: Integrate

## Brief Information

Integrate XY data

This feature is updated in 8.0 SR5. For more details, please refer to Release Notes. Updated in 8.5.1

## Command Line Usage

1. integ1 iy:=(Col(1), Col(2));
2. integ1 iy:=Col(2) type:=abs;
3. integ1 iy:=Col(2) area:=dArea;
4. integ1 iy:=Col(2) rd:=[<active>]<new>!;

## Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Input iy

Input

XYRange

<active>
Specify the input data to be integrated
Use End Points Straight Line as Baseline baseline

Input

int

0
Specify whether to create a straight line that crosses the end points and use it as the baseline for the integration.
Area Type type

Input

int

0
Specify the integral area type. Please see more details in the More Information part below.

Option list:

• math:Mathematical Area
The area is the algebraic sum of trapezoids.
• abs:Absolute Area
The area is sum of absolute trapezoid values.
Output Quantities quantities

Input

TreeNode

<unassigned>
Specify the quantities to be outputted when rd is selected. See more details in Dialog Options table: Output Quantities on this page
Integral Curve Data oy

Output

XYRange

(<input>,<new>)
Specify the range of the cumulative result. See the syntax here.
Integration Result rd

Output

[<input>]<new>
Controls output of the Integration Result.
Plot Integral Curve plot

Input

int

0

Specify whether to plot the integral curve, and where to plot the integral curve.

Option list:

• none:None
Do not plot the integral curve.
• new:New Graph
Plot the integral to a new graph.
• source:Source Graph
Plot the integral to the source graph. This option is available when the source data is from the graph.
Beginning X x1

Output

double

<unassigned>
Specify whether to output the beginning X value.
Ending X x2

Output

double

<unassigned>
Specify whether to output the ending X value.
Index for Beginning X i1

Output

int

<unassigned>
Specify whether to output the index for beginning X.
Index for Ending X i2

Output

int

<unassigned>
Specify whether to output the index for ending X.
Area of the Integration area

Output

double

<unassigned>
Specify whether to output the integration area.
Maximum Height y0

Output

double

<unassigned>
Specify whether to output the maximum Y value in source curve.
X Value in Maximum Height x0

Output

double

<unassigned>
Specify whether to output the X value that corresponds to the maximum height.
Peak Width at Half Height dx

Output

double

<unassigned>
Specify whether to output the peak width at half height of the source curve.
tr

Output

TreeNode

<optional>
Use to store output quantities (x1, x2, i1, i2, etc.) when there are multiple XY input ranges
Rescale Source Graph rescale

Input

int

0
Specify whether to rescale the source graph when the integral is plotted into it. This check-box is available when the Plot Integral Curve is Source Graph.

## Description

This X-Function performs integration on input data. It can calculate the Mathematical Area (the algebraic sum of trapezoids) or an Absolute Area (the sum of absolute trapezoid values). Missing values are ignored.

## Examples

If you want to integrate data with the absolute area method and plot the integral curve, you can do the following:

1. Import the file, <Origin Program Folder>\Samples\Mathematics\Sine Curve.dat.
2. Highlight the data columns. Select Analysis: Mathematics: Integrate to bring up the Mathematics: integ1 dialog box.
3. Select Absolute Area with the Area Type drop-down list.
4. Set the Plot Integral Curve drop-down list to New Graph.
5. After clicking OK, a new column with the integration values should be added to the source worksheet and a graph with integral curve should be created. 