Re: Change integral variables

• To: mathgroup at smc.vnet.net
• Subject: [mg88222] Re: Change integral variables
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Tue, 29 Apr 2008 06:46:41 -0400 (EDT)
• References: <fv1fep$es1$1@smc.vnet.net>

Budaoy schrieb:
> In Mathematica, how can I change integral variables? For example in
> integration:
>
> Integrate[Sin[Sqrt[x]], x] if I want to use t^2=x to instead x in the
> integral, how can I achieve this?
>
> PS: Does Mathematica have a inertial form of some symbolic command,
> for instance, the above integration, if I only want an integration
> form but not an answer, what can I do?
>
> Thanks.
>

I don't know of any inertial form to do this, but there are two
possiblities:

In=  f[x_] := Sin[Sqrt[x]];
Integrate[f[x], x]
ii = f[x] dx
tRule = {x -> t^2, dx -> 2 t}
it = Simplify[(ii /. tRule), t >= 0]

Out= ...
2 dt Sin[t]

The other possibility is David Park's Presentations package, which
includes a "StudentsIntegral". You would write then:

i1=integrate[Sin[Sqrt[x]],x]

it=i1//ChangeIntegralVariable[t->Sqrt[x],x,
DirectSubstitution->{x->t^2}]

to get the output (I write it in LaTeX notation):

\int Sin[x] dx

Gruss Peter
--
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de



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