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