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

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 Axel Vogt Posts: 992 Registered: 5/5/07
Re: are the commercial results continuous?
Posted: Jul 14, 2012 4:53 PM

On 14.07.2012 21:44, Nasser M. Abbasi wrote:
> On 7/14/2012 11:13 AM, clicliclic@freenet.de wrote:
>

>> I thought such a definite integral could be readily checked using
>> Wolfram Alpha, but I was mistaken. While Alpha allows one to produce the
>> Mathematica antiderivative with the jump near x = 0.589, it repeatedly
>> times out on:
>>
>> Integrate[(1 + x + 3*x^2)/((3 - 2*x + x^2)^2*Sqrt[2 + x^2]), {x,0,1}]
>>
>> Hence my question: What is finally returned for this definite integral
>> by a regular installation (any subversion will do) of Mathematica 8?

>
> hello Matrin;
>
> It took about 1 to 2 minutes on my PC. The result is too large
> to post here, so I copied the ouput cell as text and put it in a
> text file here for you to look at, and also a partial screen shot
> of the result. Using Mathematica 8.04 on windows 7
>
> http://12000.org/tmp/july_14_2012/result.txt
> http://12000.org/tmp/july_14_2012/screen_shot.png
>
> When I evaluate the result of the integral above numerically,
> where 'sol' below is the result of your integral, I get:
>
> In[22]:= N[sol]
> Out[22]= -0.711875+7.96585*10^-15 I
>
> anything else you'd like me to try, please let me know.
>
> regards,
> --Nasser
>

Hm: the integrand is positive ... Very roughly it is like the
line 0.6*x + 0.1, so the integral is ~ 0.4 (as a magnitude).