"Problema 5"

"=== 1. Sólido D ==="

"1.1. Gráfico de D en el plano X-Y:"
ContourPlot[{(x^2)-(y^2)==1,(x^2)-(y^2)==5,x y==4,x y==1},{x,0,15},{y,-5,10}]

"1.2. Gráfico de D en Z (suponiendo m=1):"
ContourPlot3D[{x+y+3 z==2,x+y+3 z==4},{x,0,15},{y,-5,10},{z,-9,5},AxesLabel->{"X","Y","Z"},Mesh->None,FaceGrids->{{0,0,-1},{-1,0,0},{0,1,0}},FaceGridsStyle->Directive[Dashed]]

"1.3. Momento de inercia en Z:"
J1=(1/(6 ((x^2)+(y^2)))); (* Jacobiano *)
d1=g[u]; (* Densidad *)
Izd=Integrate[J1 d1 ((x^2)+(y^2)),{u,1,5},{v,1,4},{w,2,4m}]


"=== 2. Sólido E ==="

"2.1. Gráfico de E en el plano X-Y:"
ContourPlot[{y==-x,y==5-x,x==1,x==5},{x,-2,8},{y,-8,8}]

"2.2. Momento de inercia en Z:"
J2=1; (* Jacobiano *)
d2=(k/((x^2)+(y^2))); (* Densidad *)
Ize=Integrate[J2 d2 ((x^2)+(y^2)),{u,1,5},{v,0,5},{w,0,g[u]}]