1 The curve \(C\) has equation \(y = x ^ { a }\) for \(0 \leqslant x \leqslant 1\), where \(a\) is a positive constant. Find, in terms of \(a\), the coordinates of the centroid of the region enclosed by \(C\), the line \(x = 1\) and the \(x\)-axis.
1 The curve $C$ has equation $y = x ^ { a }$ for $0 \leqslant x \leqslant 1$, where $a$ is a positive constant. Find, in terms of $a$, the coordinates of the centroid of the region enclosed by $C$, the line $x = 1$ and the $x$-axis.\\
\hfill \mbox{\textit{CAIE FP1 2019 Q1}}