The diagram shows a curve for which \(\frac{dy}{dx} = -\frac{k}{x^3}\), where \(k\) is a constant. The curve passes through the points \((1, 18)\) and \((4, 3)\).

(i) Show, by integration, that the equation of the curve is \(y = \frac{16}{x^2} + 2\).

The point \(P\) lies on the curve and has \(x\)-coordinate 1.6.

(ii) Find the area of the shaded region.