Вычисление несобственных интегралов

Clear["Global`*"]
RegionPlot[0<x<1&&0<y<1&&x -y>0,{x,0,1.1},{y,0,1.1},ImageSize->Small]
Integrate[
x*Boole[0<x<1&&0<y<1&&x -y>0],{x,-Infinity,Infinity}, {y,-Infinity,Infinity} ]

Clear["Global`*"]
T=Polygon[{{0,0},{1,0},{1,1}}];
Graphics[T,ImageSize->Small]
R=RegionBoundary[T];
Integrate[x ,{x,y}∈T]
Integrate[x ,{x,y}∈R]

Clear["Global`*"]
a=1;
RegionPlot[0<x&&0<y&&x ^2+y^2<a^2,{x,0,1.1},{y,0,1.1},ImageSize->Small]
Clear[a]
Integrate[
Sqrt[x^2+y^2]*Boole[0<x&&0<y&&x ^2+y^2<a^2],{x,-Infinity,Infinity}, {y,-Infinity,Infinity} ]

Clear["Global`*"]
T=Disk[{0,0},a,{0,Pi/2}];
Graphics[T/. a->1,ImageSize->Small]
Integrate[ Sqrt[x^2+y^2],{x,y}∈T]