The diagram shows the curve \(y = (1 + x^2) e^{-\frac{1}{2}x}\) for \(x \geq 0\). The shaded region \(R\) is enclosed by the curve, the \(x\)-axis and the lines \(x = 0\) and \(x = 2\).

(i) Find the exact values of the \(x\)-coordinates of the stationary points of the curve.

(ii) Show that the exact value of the area of \(R\) is \(18 - \frac{42}{e}\).