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Re: Problems with solving integrals in Mathematica 9
*To*: mathgroup at smc.vnet.net
*Subject*: [mg130998] Re: Problems with solving integrals in Mathematica 9
*From*: "djmpark" <djmpark at comcast.net>
*Date*: Sun, 2 Jun 2013 00:29:13 -0400 (EDT)
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It looks like the 8.04 result is only correct with conditions. It is a
basic change of variable example. The Presentations Application's Student's
Integral routines with a little help from Mathematica Integrate allow us to
evaluate the integral. The integrate routine is an unevaluated Integrate
that allows us to manipulate the integral. It displays as a regular integral
but I'll just show the InputForm here. ChangeIntegralVariable does a
substitution. We then use Integrate but with the assumptions that thr f at
the endpoints are greater than zero. Mathematica does evaluate that.
<< Presentations`
integrate[D[f[x], x]/f[x], {x, 0, T}]
% // ChangeIntegralVariable[t -> f[x], x]
% // UseIntegrate[{f[0], f[T]} > 0]
integrate[f[x]^(-1) Derivative[1][f][x], {x, 0, T}]
integrate[t^(-1), {t, f[0], f[T]}]
ConditionalExpression[Log[f[T]/f[0]], 0 < f[0] < f[T]]
The routines in the Student's Integral sub-package are: integrate,
BasicIntegralTable (basic table used by students), DisplayIntegralTable,
BreakoutIntegral, OperateIntegrand, ChangeIntegralVariable,
IntegrateByParts, TrigonometricSubsitute, LimitsBracket,
EvaluateLimitsBracket, UseIntegralTable, UseIntegrate, UseNIntegrate.
The use of integrate and UseIntegrate[assumptions] is a good method for
displaying an unevaluated integral in a notebook and then evaluating it with
assumptions.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html
From: Jost Adler [mailto:jost.adler at googlemail.com]
Has anybody encountered the same problems with solving integrals in Ver. 9
as I did?
Here a very simple example:
Integrate[D[f[x], x] / f[x], {x, 0, T}]
Version 8.04 gives the correct results:
-Log[f[0]] + Log[f[T]]
In Version 9.00 as well as 9.01 this integral can't be solved. With more
complicated integrals I had the same problems. Version 8 gives a solution,
Version 9 doesn't!
Could some other Version 9 users try it.
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