Subject: Maxima asks about sign of integration(!) variable
From: Richard Fateman
Date: Wed, 25 Sep 2013 16:33:09 -0700
On 9/25/2013 4:11 PM, Jaime Villate wrote:
> expr : sqrt(1+(4*x^(1/3)-1/16*x^((-1)/3))^2)$
Mathematica, evaluating expr at -2.0
gives 2.54465 + 4.32153*i*
Maxima gives *5.0892904824535*
One does not need to go so far as integrating anything to get into
difficulties.
RJF
>
> I'd still prefer that integrate(expr,x,-8,512) gave the answer 98739/8
> (as Macsyma does) because that answer is more consistent with the
> assumptions made by other Maxima functions:
>
> float(integrate(expr,x,-8,0)+integrate(expr,x,0,512)) --> 12342.375
>
> quad_qags(expr,x,-8,512) --->
> [12342.37489449745,1.0455241317686159e-4,819,0]
>
> romberg(expr,x,-8,512) ---> 12342.59046046695
>
> subst(x=-8,expr) ---> 257/32
>
> plot2d(expr,[x,-8,512])
>
> Regards,
> Jaime
>
> On 25-09-2013 22:45, John Lapeyre wrote:
>> On 09/25/2013 09:26 PM, Richard Fateman wrote:
>>
>> > In Mathematica, the answer came out
>> > 3/16 (65697 + 127 I Sqrt[3])
>> > or 12318.2 + 41.2445 I
>> >
>> > Doing NIntegrate in Mathematica provided
>> >
>> > 12318.1 + 41.2326 I
>> >
>>
>> My nintegrate function, which calls quadpack, seems to agree more
>> with Mathematica's exact answer than it's numerical answer. I've
>> seen that more than once.
>>
>> (%i5) nintegrate(sqrt(1+(4*x^(1/3)-1/16*x^((-1)/3))^2),[x,-8,512]);
>>
>> (%o5) [41.24445772554166*%i+12318.18747666083,1.5204793641032666e-5,2268,
>> "no problems"]
>