Overview of the IntegrationTools Package
Calling Sequence
Description
List of IntegrationTools Package Commands
Examples
IntegrationTools:-command(arguments)
command(arguments)
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.
The long form, IntegrationTools:-command is always available. The short form can be used after loading the package.
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.
withIntegrationTools:
v≔Intfx,x=a..b
v≔∫abfxⅆx
typev,Integral
true
typev,DefiniteIntegral
typev,IndefiniteIntegral
false
Extract the integrand, variable of integration and range.
GetIntegrandv
fx
GetVariablev
x
GetRangev
a..b
Split a definite integral.
v≔Intsinx,x=0..2πn
v≔∫02πnsinxⅆx
Splitv,2π
∫02πsinxⅆx+∫2π2πnsinxⅆx
Splitv,2π,4π,6π
∫02πsinxⅆx+∫2π4πsinxⅆx+∫4π6πsinxⅆx+∫6π2πnsinxⅆx
Splitv,2πi,i=1..n−1
∫02πsinxⅆx+∑_j=1n−2∫2π_j2π_j+1sinxⅆx+∫2πn−12πnsinxⅆx
Perform integration by parts.
v≔Intexpxsinx,x=a..b
v≔∫abⅇxsinxⅆx
Partsv,sinx
ⅇbsinb−ⅇasina−∫abⅇxcosxⅆx
Partsv,expx
−ⅇbcosb+ⅇacosa−∫ab−ⅇxcosxⅆx
Expand an integral.
v≔Intafx+bgx+chx,x=1..2
v≔∫12afx+bgx+chxⅆx
w≔Expandv
w≔a∫12fxⅆx+b∫12gxⅆx+c∫12hxⅆx
Combine multiple integrals.
Combinew
∫12afx+bgx+chxⅆx
CombineIntfx,x=a..b+Intfx,x=b..c−Intfx,x=a..d
∫dcfxⅆx
See Also
combine
expand
int
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