Вычисление несобственных интегралов

Clear["Global`*"]
RegionPlot3D[x≥ 0&&y≥ 0&&z≥ 0&&x+y+z≤ 1,{x,-0.2,1},{y,-0.2,1},{z,-0.2,1}]
Integrate[(x+y +z)*Boole[x>0&&y>0&&z>0&&x+y+z<1],{x,-∞,∞},{y,-∞,∞},{z,-∞,∞}]

R=ImplicitRegion[x>=0&&y>=0&&z>=0&&x+y+z≤ 2,{x,y,z}];
RegionPlot3D[R]
Integrate[x+y+z,{x,y,z}∈R]

R=Ball[{0,0,0},a];
Graphics3D[R/. a->1]
Integrate[x^2+y^2+z^2,{x,y,z}∈R]