- (i) The gradient of a curve is given by
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 - \frac { 2 } { x ^ { 2 } } , \quad x \neq 0$$
Find an equation for the curve given that it passes through the point \(( 2,6 )\).
(ii) Show that
$$\int _ { 2 } ^ { 3 } \left( 6 \sqrt { x } - \frac { 4 } { \sqrt { x } } \right) d x = k \sqrt { 3 }$$
where \(k\) is an integer to be found.