On Aug 18, 6:48 pm, Golam Mortuza Hossain <gmhoss...@gmail.com> wrote:
> Hi,
>
> On Tue, Aug 18, 2009 at 8:42 PM, rjf<fate...@gmail.com> wrote:
>
> > did you mean to integrate with respect to "x^2" ?
>
> Yes.
Well then, since you meant to do that, what response would you
consider correct?
An error message, or William's interpretation of d(x^2) as 2xdx?
or something else?
>
> > Well, x^2 doesn't occur in f(x). So let's rename x^2 as y.
> > What is the integral of f(x) with respect to y?
>
> > It is y*f(x).
>
> > substituting back x^2 for y, you get x^2*f(x).
>
> Are you saying during integration maxima is not aware
> that "x^2" is the square of "x"?
Right, because your "variable of integration" is not in the integrand.
If I search for x^2 in f(x), I get no matches.
>
> Take following examples:
> ----------
> (%i4) integrate(log(x), x);
> (%o4) x log(x) - x
This is a correct usage, and the answer is correct.
>
> (%i5) integrate(log(x^2), x^2);
> 2
> (%o5) 2 x log(x)
> ----------
>
> "log" is certainly aware of it.
This is an incorrect usage. Following the recipe I gave above, I
think that
Maxima first of all simplified log(x^2) to 2*log(x). The integrand
does not
contain any x^2. y. Then the
problem is integrate(2*log(x),y). Which is 2*y*log(x). Now
substitute x^2 for y.
You get the answer above.
>
> > Certainly Maxima expects "the variable of integration" as
> > the second argument. Anything else is asking for trouble.
>
> Then maxima should throw error instead of giving a wrong
> answer silently.
Maybe. or maybe it should return the integral unevaluated. or maybe
it
should try to compute the differential.
> This is rather bizarre given maxima is known
> to be over-cautious during integration and sometime
> it asks too many questions, even something like
> --------
> (%i6) integrate(1/x, x, 0, 1);
> Is x + 1 positive, negative, or zero?
When Maxima asks questions, it is not being cautious..
The program asks questions so it can provide a correct answer.
As it happens, it sometimes asks questions when it could deduce the
answer.
This is a deficiency in the deduction system, not integration.
You are probably using an outdated Maxima, since the current one
does not ask questions, but just says the integral is divergent.
You could try integrate(1/x,x,a,b) and then it asks questions to try
to
determine if a<=0<=b.
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