Overview of the IntegrationTools Package - Maple Programming Help

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Overview of the IntegrationTools Package

 

Calling Sequence

Description

List of IntegrationTools Package Commands

Examples

Calling Sequence

IntegrationTools[command](arguments)

command(arguments)

Description

• 

The IntegrationTools package is a set of programmer tools used for low level manipulation of definite and indefinite integrals.

  

Note: This package contains tools for manipulating the data structure only and do not ensure the validity of the operation being performed. For mathematical operations on integrals, use top-level commands such as combine, expand, etc., or the Student package.

• 

At load time the IntegrationTools package defines three new types: Integral, DefiniteIntegral and IndefiniteIntegral, which can be used to access integrals involved in any given expression.

• 

Each command in the IntegrationTools package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

• 

As the underlying implementation of the IntegrationTools package is a module, it is also possible to use the form IntegrationTools:-command to access a command from the package. For more information,  see Module Members.

List of IntegrationTools Package Commands

  

The following is a list of available commands.

Change

CollapseNested

Combine

Expand

ExpandMultiple

Flip

GetIntegrand

GetOptions

GetParts

GetRange

GetVariable

Parts

Split

StripOptions

 

 

  

To display the help page for a particular IntegrationTools command, see Getting Help with a Command in a Package.

Examples

withIntegrationTools:

vIntfx,x=a..b

vabfxⅆx

(1)

typev,Integral

true

(2)

typev,DefiniteIntegral

true

(3)

typev,IndefiniteIntegral

false

(4)

Extract the integrand, variable of integration and range.

GetIntegrandv

fx

(5)

GetVariablev

x

(6)

GetRangev

a..b

(7)

Split a definite integral.

vIntsinx,x=0..2πn

v02πnsinxⅆx

(8)

Splitv,2π

02πsinxⅆx+2π2πnsinxⅆx

(9)

Splitv,2π,4π,6π

02πsinxⅆx+2π4πsinxⅆx+4π6πsinxⅆx+6π2πnsinxⅆx

(10)

Splitv,2πi,i=1..n1

02πsinxⅆx+_j=1n22π_j2π_j+1sinxⅆx+2πn12πnsinxⅆx

(11)

Perform integration by parts.

vIntexpxsinx,x=a..b

vabⅇxsinxⅆx

(12)

Partsv,sinx

ⅇbsinbⅇasinaabⅇxcosxⅆx

(13)

Partsv,expx

ⅇbcosb+ⅇacosaabⅇxcosxⅆx

(14)

Expand an integral.

vIntafx+bgx+chx,x=1..2

v12afx+bgx+chxⅆx

(15)

wExpandv

wa12fxⅆx+b12gxⅆx+c12hxⅆx

(16)

Combine multiple integrals.

Combinew

12afx+bgx+chxⅆx

(17)

CombineIntfx,x=a..b+Intfx,x=b..cIntfx,x=a..d

cdfxⅆx

(18)

See Also

combine

expand

int