Subject: Maxima asks about sign of integration(!) variable
From: Jaime Villate
Date: Thu, 26 Sep 2013 00:11:38 +0100
expr : sqrt(1+(4*x^(1/3)-1/16*x^((-1)/3))^2)$
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"]