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IntegrationTools

  

Change

  

perform a change of variables in an integral

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Change(v, c)

Change(v, c, y)

Parameters

v

-

expression involving definite or indefinite integrals

c

-

a transformation or a list or set of transformations

y

-

a list of the new variables

Description

• 

The Change command performs a change of variables in the integrals involved in v.

• 

The second parameter c is the transformation (or list of transformations or set of transformations) in the form x=f(u) (assuming x is the original variable and u is the new variable). Implicit transformations (g(x)=h(u)) can be given as long as it is possible to unambiguously rewrite it as an explicit transformation.

• 

The third parameter y is required only if the number of new symbols in the transformation is not equal to the number of old variables in v.

Examples

withIntegrationTools:

V∫abfx2ⅆx

V:=∫abfx2ⅆx

(1)

ChangeV,x=u2

∫ab2fu4uⅆu

(2)

There are two new symbols in the transformation so the third argument is required.

V∫abfxⅆx

V:=∫abfxⅆx

(3)

ChangeV,x=uc,u

∫c+ac+bfucⅆu

(4)

Multivariate integral.

V∫cd∫abfx2gyⅆxⅆy

V:=∫cd∫abfx2gyⅆxⅆy

(5)

ChangeV,x=u2,y=v2

∫cd2∫ab2fu4gv2uⅆuvⅆv

(6)

See Also

IntegrationTools

PDEtools[dchange]

 


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