10 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 16 } { x ^ { 3 } }\), and \(( 1,4 )\) is a point on the curve.
- Find the equation of the curve.
- A line with gradient \(- \frac { 1 } { 2 }\) is a normal to the curve. Find the equation of this normal, giving your answer in the form \(a x + b y = c\).
- Find the area of the region enclosed by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 2\).
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