(* Centroid of semicircle wire *)

(* Parametrization of the semicircle *)
q={Sin[t],Cos[t]}
qp=D[q,t]

(* Centroid *)
a=Expand[Norm[qp]]
m=Integrate[a,{t,0,Pi}] 
mx=Integrate[q[[1]] a,{t,0,Pi}] 
xbar=mx/m 
my=Integrate[q[[2]] a,{t,0,Pi}] 
ybar=my/m

plot1=ParametricPlot[q,{t,0,Pi}];
Show[plot1,Graphics[{PointSize[0.05],Point[{xbar,ybar}]}]]