On Wednesday, March 13, 2019 at 7:11:02 PM UTC-4, Emmanuel Charpentier
wrote:
>
> This integral turns out to be anything but trivial.
>
> Neither Sympy, Giac nor Fricas can solve it, in its original form nor in
> polar coordinates. BTW, neither Mathematica nor Rubi running on Mathematica
> can solve it in neither form.
>
> The analytic answer given (semi-)trivially by Maxima is probably false.
> I'm unable to check it.
>
Following up, does this computation make any sense? Presumably this is the
core issue.
sage: maxima_console()
<snip>
(%i1) z:sqrt(1-x^2-y^2);
2 2
(%o1) sqrt((- y ) - x + 1)
(%i2) display2d:false;
(%o2) false
(%i3) integrate(z,y);
Is (x-1)*(x+1) positive or negative?
n;
(%o3) (-(x^2*asin(y/sqrt(1-x^2)))/2)+asin(y/sqrt(1-x^2))/2+(y
*sqrt(
(-y^2)-x^2+1))
/2
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