(* We compute the volume of a solid in the first octant bounded by x^2+y^2=1, y=z,x=0,z=0 *)
ContourPlot3D[{x==0,z==0,x^2+y^2==1,z==y},{x,0,1},{y,0,1},{z,0,1}]
RegionPlot3D[x≥0 && z≥0 && x^2+y^2≤1 && z≤y,{x,0,1},{y,0,1},{z,0,1}, PlotPoints->50, PlotStyle->Opacity[.6]]

(* Using a double integral *)
Integrate[y,{y,0,Sqrt[1-x^2]}]
Integrate[%,{x,0,1}]

(* Using a triple integral *)
Integrate[1,{z,0,y}]
Integrate[%,{y,0,Sqrt[1-x^2]}]
Integrate[%,{x,0,1}]