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Topic: Problems with solving integrals in Mathematica 9
Replies: 1   Last Post: Jun 2, 2013 12:24 AM

 David Park Posts: 1,560 Registered: 5/19/07
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 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@comcast.net
http://home.comcast.net/~djmpark/index.html

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.