Definite integrals and asksign



Hi Ray

On Fri, 08 Dec 2006 09:01:07 -0500, Raymond Toy wrote:

>>>>>> "Neilen" == Neilen Marais <nmarais at sun.ac.za> writes:
 
>     Neilen> If I succesively take indefinite integrals and manually substitute the bounds I
>     Neilen> get the same answer, without any asksign questions (I omitted some of the
>     Neilen> intermediate results to save space):
> 
>     Neilen> (%i34) integrate(tmpp, x3);
>     Neilen> (%o34) (x2/2+x1/2)*sin((%pi*x2)/2+(%pi*x1)/2-%pi/4)*x3(%i35) ev(%, x3:1-x2-x1)
>     Neilen> - ev(%,x3:0);
> 
> I did not investigate the exact reason for why you asked for the sign
> of various things, but you should note that definite integrals are
> often transformed to different forms to evaluate it.  That is,
> definite integration does not necessarily find the indefinite integral
> and substitute in the limits, which is what you are doing here by
> hand.  If you do integrate(tmpp, x3, 0, 1-x1-x2), you will be asked
> for the sign of x1+x2-1.

Fair enough, I guess my real question is then, would I be making a mathematical
mistake by substituting the limits without knowing the sign of x1+x2-1? 

> If I do this:
> 
> assume(x1>0, x2 > 0, x3 > 0, x1 < 1, 1-x1-x2> 0);
> 
> the triple integral only asks for the sign of cos(%pi*x1/2) and
> sin(%pi*x1/2).  I guess that's a deficiency in maxima that it doesn't
> know the sign of those.

Would I be correct in guessing that Maxima would have been able to figure out
what you passed in the assume() above if it had a built in multiple integral
routine that could consider all the integral limits simultaneously? 
 
> Ray

Thanks
Neilen

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