A thin, non-uniform rod of total mass \(M\) and length \(L\) lies along the positive \(x\)-axis between \(x = 0\) and \(x = L\). The linear mass density of the rod decreases exponentially from the left end according to the function \(\lambda(x) = \lambda_0 e^{-x/L}\), where \(\lambda_0\) is a positive constant. Which of the following expressions correctly represents the center-of-mass coordinate \(x_{\text{cm}}\) of the rod measured from \(x = 0\)?