9. (i) Evaluate $$\int _ { 1 } ^ { 3 } ( 3 - \sqrt { x } ) ^ { 2 } d x$$ giving your answer in the form \(a + b \sqrt { 3 }\), where \(a\) and \(b\) are integers.
(ii) The gradient of a curve is given by $$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } + 4 x + k$$ where \(k\) is a constant. Given that the curve passes through the points \(( 0 , - 2 )\) and \(( 2,18 )\), show that \(k = 2\) and find an equation for the curve.