9 The curve \(C\) has equation \(y = x ^ { \frac { 3 } { 2 } }\). Find the coordinates of the centroid of the region bounded by \(C\), the lines \(x = 1 , x = 4\) and the \(x\)-axis.
Show that the length of the arc of \(C\) from the point where \(x = 5\) to the point where \(x = 28\) is 139 .
9 The curve $C$ has equation $y = x ^ { \frac { 3 } { 2 } }$. Find the coordinates of the centroid of the region bounded by $C$, the lines $x = 1 , x = 4$ and the $x$-axis.
Show that the length of the arc of $C$ from the point where $x = 5$ to the point where $x = 28$ is 139 .
\hfill \mbox{\textit{CAIE FP1 2011 Q9}}