On Sat, 26 Jan 2008 06:39:09 -0500, quasi <quasi@[EMAIL PROTECTED]
> wrote:
>On Sat, 26 Jan 2008 03:07:45 -0800 (PST), Vladimir Bondarenko
><vb@[EMAIL PROTECTED]
> wrote:
>
>>----------------------------------------------------------------
>>
>>An exact 1-D integration challenge - 48 -
>>(go and give a kick to all stupid CASs!)
>>
>>http://groups.google.com/group/sci.math.symbolic/browse_thread/thread/28416525f0de8f90/1d8cd83e96cb7f63?#1d8cd83e96cb7f63
>>
>>----------------------------------------------------------------
>>
>>N[Integrate[
>>
>> Sqrt[Sqrt[2] + Sqrt[z] + Sqrt[2 + 2 Sqrt[2] Sqrt[z] + 2 z]],
>>
>> {z, 0, 1}]]
>>
>>----------------------------------------------------------------
>>VERSION OUTPUT RESOLUTION
>>----------------------------------------------------------------
>>
>>Mathematica 6.0 2.67602 <-------------------------------- BUG
>>
>>Mathematica 5.2 3.66533 <-------------------------------- BUG
>
>Let f(z) = sqrt(sqrt(2) + sqrt(z) + sqrt(2 + 2*sqrt(2)*sqrt(z) + 2*z))
>
>Then it's completely obvious that f has domain [0,infinity) and that
>is strictly increasing.
>
>Hence the integral of f on the interval [0,1] must be strictly between
>f(0) and f(1).
>
>Approximately, we have
>
> f(0) = 1.681792831
>
>and
>
> f(1) = 2.242172940
>
>which makes it clear that Mathematica's outputs are ridiculous.
>
>Maple 9.5 gives a result of 2.062759840, which at least seems
>reasonable. Whether it's correct or not, I'm not sure.
>
>quasi
A CAS should never return a wrong answer. Returning no answer is
better than a wrong one.
For this example in particular, Mathematica really has no excuse for
getting it wrong. It's not like the function has wild variations which
might throw off a numerical integration. This is a positive,
increasing function, easily evaluated. For a CAS, the numerical
integration of such a function should be effortless.
quasi
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