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\includegraphics[max width=\textwidth, alt={}, center]{d71002bb-b6f0-42a3-89fb-f2769d5c3779-3_791_885_1281_630}
The diagram shows a curve for which \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { k } { x ^ { 3 } }\), where \(k\) is a constant. The curve passes through the points \(( 1,18 )\) and \(( 4,3 )\).
- 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.
- Find the area of the shaded region.