Clear["Global`*"]

<< DifferentialForms`

Izz1=0.001(*in kg*m^2*)

Izz2=0.001(*in kg*m^2*)

m1 = 0.181 (*in kg*)

m2 = 0.181(*in kg*)

L1 = 0.250 (*in m*)

L2 = 0.250 (*in m*)

g1[{Th1_,Th2_}]={{Izz1+Izz2+(m2*(2*((L2*Cos[Th1+Th2])/2+L1*Cos[Th1])^2+2*((L2*Sin[Th1+Th2])/2+L1*Sin[Th1])^2))/2+(m1*((L1^2*Cos[Th1]^2)/2+(L1^2*Sin[Th1]^2)/2))/2,Izz2+(m2*(L2*Sin[Th1+Th2]*((L2*Sin[Th1+Th2])/2+L1*Sin[Th1])+L2*Cos[Th1+Th2]*((L2*Cos[Th1+Th2])/2+L1*Cos[Th1])))/2} ,{Izz2+(m2*(L2*Sin[Th1+Th2]*((L2*Sin[Th1+Th2])/2+L1*Sin[Th1])+L2*Cos[Th1+Th2]*((L2*Cos[Th1+Th2])/2+L1*Cos[Th1])))/2,Izz2+(m2*((L2^2*Cos[Th1+Th2]^2)/2+(L2^2*Sin[Th1+Th2]^2)/2))/2}} (*in kg*m^2*)

eta1 = Sqrt[Det[g1[{Th1,Th2}]]]*Wedge[d[Th1],d[Th2]] (*in kg*m^2*)

T2Chain1 = Chain[{Th1 -> q, Th2 -> s},{q, 0, 2*Pi},{s,0,2*Pi}] (*in rad^2*)

T2Volume1 = NumberForm[N[Integral[eta1,T2Chain1]],3] (*in kg*m^2*)

w1 = {1.0934,0} (*in rad*)

w2 = {0.3236, 0.1158} (*in rad*)

g2[{Th1_,Th2_}]={{1,0},{0,1} }(*in kg*m^2*)

eta2 = Sqrt[Det[g2[{Th1,Th2}]]]*Wedge[d[Th1],d[Th2]] (*in kg*m^2*)

T2Chain21 = Chain[{Th1 -> q, Th2 -> s},{q, 0, w2[[1]]},{s,0,(w2[[2]]/w2[[1]])*q}] (*in rad^2*)

T2Volume21 = NumberForm[N[Integral[eta2,T2Chain21]],3] (*in kg*m^2*)

T2Chain22 = Chain[{Th1 -> q, Th2 -> s},{q, w2[[1]], w1[[1]]},{s,0, w2[[2]]}] (*in rad^2*)

T2Volume22 = NumberForm[N[Integral[eta2,T2Chain22]],3] (*in kg*m^2*)

T2Chain23 = Chain[{Th1 -> q, Th2 -> s},{q, w1[[1]], w1[[1]]+w2[[1]]},{s,(w2[[2]]/w2[[1]])*(q-w1[[1]]), w2[[2]]}] (*in rad^2*)

T2Volume23 = NumberForm[N[Integral[eta2,T2Chain23]],3] (*in kg*m^2*)

T2Volume2 = T2Volume21 + T2Volume22 + T2Volume23

N[Round[(0.0187 + 0.0891 + 0.0187)*1000]/1000]

N[Round[Cross[{w1[[1]],w1[[2]],0},{w2[[1]],w2[[2]],0}][[3]]*1000]/1000]