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
>
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>
>N[Integrate[
>
> Sqrt[Sqrt[2] + Sqrt[z] + Sqrt[2 + 2 Sqrt[2] Sqrt[z] + 2 z]],
>
> {z, 0, 1}]]
>
>----------------------------------------------------------------
>VERSION OUTPUT RESOLUTION
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>
>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
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