(*Doppelintegral*)

Plot3D[Exp[x+y],{x,0,1},{y,0,1}]
Integrate[Exp[x+y],{x,0,1},{y,0,1}]

Integrate[Exp[x+y],{x,0,1},{y,0,x}]

Integrate[Integrate[Exp[x+y],x],y]

Integrate[1  Boole[x^2+y^2≤1],{x,-1,1},{y,-1,1}]
Integrate[1  Boole[x^2+y^2≤1],{x,-2,2},{y,-2,2}]

Integrate[x*y Boole[x^2+y^2≤1],{x,-2,2},{y,-2,2}]

FlSattel=Plot3D[x*y,{x,-2,2},{y,-2,2}];
Flzyl=ContourPlot3D[x^2+y^2==1,{x,-2,2},{y,-2,2},{z,-5,5},ContourStyle->Directive[Orange,Opacity[0.5]]];
Flxy=Plot3D[0,{x,-2,2},{y,-2,2},PlotStyle->Directive[Yellow,Specularity[White,20],Opacity[0.5]]];
Show[{Flxy,FlSattel},PlotRange->All,Boxed->False]
Show[{Flzyl,FlSattel},PlotRange->All,Boxed->False]

Integrate[x^2+y^2 ,{x,0,1},{y,0,1}]
Integrate[x^2+y^2 Boole[x^2+(y-0.5)^2≤0.25],{x,0,1},{y,0,1}]