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Re: Problems with solving integrals in Mathematica 9
Posted:
Jun 2, 2013 12:24 AM


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 subpackage 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@comcast.net http://home.comcast.net/~djmpark/index.html
From: Jost Adler [mailto:jost.adler@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.



