IntegrationTools
Change
perform a change of variables in an integral
Calling Sequence
Parameters
Description
Examples
Change(v, c)
Change(v, c, y)
v
-
expression involving definite or indefinite integrals
c
a transformation or a list or set of transformations
y
a list of the new variables
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.
withIntegrationTools:
V≔Intfx2,x=a..b
V≔∫abfx2ⅆx
ChangeV,x=u2
∫ab2fu4uⅆu
There are two new symbols in the transformation so the third argument is required.
V≔Intfx,x=a..b
V≔∫abfxⅆx
ChangeV,x=u−c,u
∫c+ac+bfu−cⅆu
Multivariate integral.
V≔IntIntfx2gy,x=a..b,y=c..d
V≔∫cd∫abfx2gyⅆxⅆy
ChangeV,x=u2,y=v2
∫cd2∫ab2fu4gv2uⅆuvⅆv
See Also
PDEtools[dchange]
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