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Topic: are the commercial results continuous?
Replies: 59   Last Post: Jul 30, 2012 4:28 PM

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Nasser Abbasi

Posts: 5,688
Registered: 2/7/05
Re: are the commercial results continuous?
Posted: Jul 17, 2012 1:21 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 7/16/2012 4:11 PM, Nasser M. Abbasi wrote:
> On 7/16/2012 3:50 PM, clicliclic@freenet.de wrote:
>

>>
>
> Here they are, using V 8.04 on windows:
>
> ---- first one -----------------
> Clear[x];
> integrand=(2+3*x-2*x^2)/((1+x+x^2)^2*Sqrt[1-x+x^2]);
> sol=Integrate[integrand,{x,-1,0}]
> In[3]:= N[sol]
> Out[3]= -1.60465+0. I
>
> In[5]:= sol2=NIntegrate[integrand,{x,-1,0},WorkingPrecision->20]
> Out[5]= 0.061431946878726698474
> -----------------------
>
> --- second example ------
> integrand=(1-x+3*x^2)/((1+x+x^2)^2*Sqrt[1-x+x^2]);
> sol=Integrate[integrand,{x,-1,0}]
>
> In[8]:= N[sol]
> Out[8]= -1.84016-1.4803*10^-16 I
>
> In[9]:= sol2=NIntegrate[integrand,{x,-1,0},WorkingPrecision->20]
> Out[9]= 2.6027195829817573677
> -----------------------


I upgraded to Maple 16, and tried these on it. Maple seems to handle
these type of integrals better. Not only the expressions came out
smaller in size, but evaluating the symbolic result numerically
using evalf(sol) produced the correct result without having to do
numerical integration with increased precision.

--- example 1 Maple 16-----
integrand:=(2+3*x-2*x^2)/((1+x+x^2)^2*sqrt(1-x+x^2));
sol:=int(integrand,x=-1..0);

-3/2+(1/16)*sqrt(2)*sqrt(3)*ln(3*sqrt(2)+4)-(1/16)*sqrt(2)*sqrt(3)*
ln(3*sqrt(2)-4)+(1/2)*sqrt(3)-(1/16)*sqrt(2)*sqrt(3)*ln(sqrt(2)*
sqrt(3)+2)+(1/16)*sqrt(2)*sqrt(3)*ln(sqrt(2)*sqrt(3)-2)+(3/8)*
sqrt(2)*arctan(sqrt(2))

evalf(sol);
0.0614319480
--------------------------

---- example 2 Maple 16------------
integrand:=(1-x+3*x^2)/((1+x+x^2)^2*sqrt(1-x+x^2));
sol:=int(integrand,x=-1..0);

1+(1/12)*sqrt(2)*sqrt(3)*ln(3*sqrt(2)+4)-(1/12)*sqrt(2)*sqrt(3)*
ln(3*sqrt(2)-4)-(1/12)*sqrt(2)*sqrt(3)*ln(sqrt(2)*
sqrt(3)+2)+(1/12)*sqrt(2)*sqrt(3)*ln(sqrt(2)*sqrt(3)-2)+sqrt(2)*arctan(sqrt(2))

evalf(sol);
2.602719583
---------------------------------

I am glad to also say that the copy using the mouse from the
Maple worksheet seems to be working very well now in V 16. Now
I can copy things out like I did above with no problem. Before,
this did not work well at all.

--Nasser







Date Subject Author
6/24/12
Read are the commercial results continuous?
clicliclic@freenet.de
6/24/12
Read Re: are the commercial results continuous?
Axel Vogt
6/24/12
Read Re: are the commercial results continuous?
Axel Vogt
6/24/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
6/24/12
Read Re: are the commercial results continuous?
Axel Vogt
6/24/12
Read Re: are the commercial results continuous?
Richard Fateman
6/24/12
Read Re: are the commercial results continuous?
Nasser Abbasi
6/25/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
6/29/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
6/30/12
Read Re: are the commercial results continuous?
Herman Rubin
7/14/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/14/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/14/12
Read Re: are the commercial results continuous?
Axel Vogt
7/14/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/14/12
Read Re: are the commercial results continuous?
Peter Pein
7/14/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/14/12
Read Re: are the commercial results continuous?
Peter Pein
7/14/12
Read Re: are the commercial results continuous?
Peter Pein
7/15/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/15/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/15/12
Read Re: are the commercial results continuous?
Axel Vogt
7/16/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/16/12
Read Re: are the commercial results continuous?
Axel Vogt
7/16/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/16/12
Read Re: are the commercial results continuous?
Axel Vogt
7/16/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/16/12
Read Re: are the commercial results continuous?
Axel Vogt
7/16/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/16/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/16/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/17/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/17/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/17/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/18/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/18/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/21/12
Read mathematicomaplological conclusion
clicliclic@freenet.de
7/21/12
Read Re: mathematicomaplological conclusion
Axel Vogt
7/21/12
Read Re: mathematicomaplological conclusion
clicliclic@freenet.de
7/22/12
Read Re: mathematicomaplological conclusion
Axel Vogt
7/22/12
Read Re: mathematicomaplological conclusion
clicliclic@freenet.de
7/22/12
Read Re: mathematicomaplological conclusion
Axel Vogt
7/29/12
Read Re: are the commercial results continuous?
Peter Pein
7/29/12
Read Re: are the commercial results continuous?
Axel Vogt
7/30/12
Read Re: are the commercial results continuous?
Nasser Abbasi
7/30/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
7/29/12
Read Re: are the commercial results continuous?
Nasser Abbasi
6/25/12
Read Re: are the commercial results continuous?
A N Niel
6/25/12
Read Re: are the commercial results continuous?
Richard Fateman
6/25/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de
6/25/12
Read Re: are the commercial results continuous?
Herman Rubin
6/28/12
Read Re: are the commercial results continuous?
Herman Rubin
6/28/12
Read Re: are the commercial results continuous?
Richard Fateman
6/30/12
Read Re: are the commercial results continuous?
Herman Rubin
6/25/12
Read Re: are the commercial results continuous?
clicliclic@freenet.de

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