Subject: integrate ( exp (x^3), x, 0, 1) still wrong
From: Edwin Woollett
Date: Sat, 12 May 2012 12:01:05 -0700
On May 12, 2012, Raymond Toy wrote:
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>> case exp(x^5) over (1,2)
>> domain:complex greatly improves answer
>> but large incorrect imaginary part
>> and real part only accurate to two sig. figures.
>
>Yes, that's a problem. gamma_incomplete(1/5,-32) is not very accurate.
> This can probably solved, but I'm not sure. Using bigfloats with 32
>digits gives a much better answer.
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I have incorporated domain:complex and bigfloat
evaluation of symbolic integrate result inside my
nint code (which uses mfloat which I have already
displayed on the mailing list). This goes now for
16 significant figure accuracy:
using my mfloat(expr,16) inside nint:
(%i1) load(nint);
quad_util.mac
mydefint.mac
quad1d.mac
quad2d.mac
(%o1) "c:/work2/nint.mac"
(%i2) domain;
(%o2) complex
(%i3) nint(exp(x^5),x,1,2);
(%o3) 1.0132394896940183E+12
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which agrees with wolfram alpha.
Ted