On Tuesday, March 27, 2012 4:25:48 PM UTC-4, david.guichard wrote:
>
> I've tried this on my 4.6 sage and on 5.0 beta; the main sagenb.org is
> not returning calculations for me. Both 4.6 and 5.0 have the same error.
> This double integral calculation is correct:
>
> var("r t")
> f=integral(sqrt(1-r^2*cos(t)^2)*r,r,0,1)
> g=integral(f,t)
> g; g(t=pi/4)-g(t=0)
>
> but this one is not:
>
> integral(f,t,0,pi/4)
>
>
I tried this out a bit in Maxima, and it seems that there it's even easier
to get the wrong result. I suspect that sqrt(-cos(t)^2 + 1) might be in a
situation where it's considered sin(t) or something...
in Sage:
sage: integral(f,t)
-1/3*(tan(t)^2 + 2)/sqrt(tan(t)^2 + 1) + 1/3*tan(t)
in Maxima:
(%i10) g
;
(%o10) ((sin(3 t) + sin(t)) sin(4 t) + (cos(3 t) + cos(t)) cos(4 t)
+ 6 sin(2 t) sin(3 t) + (6 cos(2 t) + 1) cos(3 t) + 6 sin(t) sin(2 t)
2
+ 6 cos(t) cos(2 t) + cos(t))/(3 (2 sin (3 t) + 4 sin(t) sin(3 t)
2 2 2 tan(t)
+ 2 cos (3 t) + 4 cos(t) cos(3 t) + 2 sin (t) + 2 cos (t))) + ------
3
Not sure what's going on with this, but I really suspect there's some
unfortunate simplifications somewhere. I'm sorry I don't have time to look
more into this right now :(
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