Numerical Integration dialog box

 

Use this dialog box to estimate one-dimensional integrals of empirical data through closed or open intervals.

 

Refer to Integration Type on this topic for additional information on this subject.

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid extents in the Input Range box.

 

Input Range

Type in this box the range of cells containing the data you want to use as input for this command.

 

Values Context

Specifies the context of the values indicated by the Input Range box.

 

Evenly Spaced

Select this option to specify that the data indicated by the Input Range box is spaced at equal intervals of an independent variable.

 

Arbitrarily Spaced

Select this option to specify that the data indicated by the Input Range box is spaced at arbitrary intervals of an independent variable.

 

 

Values in Rows

Check this box to indicate that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Plot

Check this box to plot the results of this operation.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Options

 

Integration Type

Indicates the section for which integration is to take place. Select one of:

 

Closed

Select this option to integrate the selected series throughout its length.

 

Open

Select this option to integrate the selected series at a specified interval.

 

Method

Specifies the method that will be used to carry out integration. Select one of the following:

 

Cubic Splines

Select this option to carry integration using interpolating cubic splines.

Refer to Cubic Spline Type and Spline End Conditions in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Piecewise Polynomials

Select this option to carry integration using interpolating piecewise polynomials.

 

Polynomial Interpolation

Select this option to carry integration using polynomial interpolation.

 

Cubic Spline Type

Specifies the type of cubic spline that will be used to carry spline integration. Select one of the following:

 

Clamped Spline

Select this option to carry integration using splines where the end-point conditions refer to the value of the first derivative of the series at its extreme points.

Refer to Complete Cubic Splines for additional information on this subject.

 

Natural Spline

Select this option to carry integration using splines where the end-point conditions refer to the value of the second derivative of the series at its extreme points.

Refer to Natural Cubic Splines for additional information on this subject.

 

Third Derivative

Select this option to carry integration using splines where the end-point conditions refer to the value of the third derivative of the series at its extreme points.

Refer to Splines With Specified End-Point Third Derivatives for additional information on this subject.

 

Not-a-Knot Spline

Select this option to carry integration using splines where where the third derivative of the spline function is continuous at the second and second-to-last nodes.

Refer to Not-a-knot Splines for additional information on this subject.

 

Refer to Spline End Conditions in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Initial x

Type in this box the initial x-coordinate value of the input series.

 

 

Delta x

Type in this box the increment of successive x-coordinate values.

 

 

x-Values Range

Specifies a worksheet range containing the x-values related to the functional values of the input range.

Refer to Arbitrarily Spaced on this topic for additional information on this subject.

 

Integration Interval

Specifies the integration interval.

 

Initial x

Type in this box the x-coordinate value of the interval where integration is to start.

 

Final x

Type in this box the x-coordinate value of the interval where integration is to end.

 

Spline End Conditions

Specifies the conditions at the first and last points of the series.  These boxes will have different meanings depending on the type of selected spline (Cubic Spline).

 

Start Point Condition

Type in this box the value of the condition of the first or start point of the series. For example, you could type a value of zero (0) for the first derivative of the first point of the series in relation to clamped splines to make the series appear as having extrema at this point.

 

End Point Condition

Type in this box the value of the condition of the last or end point of the series. For example, you could type a value of one (1) for the first derivative of the last point of the series in relation to clamped splines to make the series appear as increasing at this point.

 

Refer to Cubic Spline Type in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Piecewise Polynomial Parameters

Specifies the parameters for integrating using piecewise polynomials.

 

Polynomial Degree

Specifies the degree of the interpolating piecewise polynomials. Type in this box a value in the range of 1 through 15, or the length of the selected series less one if the series length is smaller than 16.

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.