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*)

g[{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*)

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

T2Chain = Chain[{Th1 -> q, Th2 -> s},{q, 0, 2*Pi},{s,0,2*Pi}] (*in rad^2*)

T2Volume = Abs[N[Integral[eta,T2Chain]]] (*in kg*m^2*)

NumberForm[%,3]