“Digits = 10”
Код:
> f:= 1/(x^4+y^4)^(1/3):
> I1:= int(f, [x=-1..1, y=-1..1]);
I1 := 3/4*(-3^(1/2)*Pi*2^(1/2)*GAMMA(2/3)*cos(5/12*Pi)+2*3^(1/2)*Pi*2^(1/2)*GAMMA(2/3)*sin(1/12*Pi)-16*hypergeom([1/12, 1/4, 1/3],[13/12, 5/4],-1)*GAMMA(11/12)*GAMMA(3/4)*sin(1/12*Pi)*cos(5/12*Pi))/sin(1/12*Pi)/cos(5/12*Pi)/GAMMA(11/12)/GAMMA(3/4)
> evalf(I1);
11.39721951
> eps:= 10^(-12);
> evalf(Int(f, [x=-1..-eps, y=-1..1])) + evalf(Int(f, [x=eps..1, y=-1..1]));
11.39721927
[Редактирование: один пропущенный ">" добавил]