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\includegraphics[max width=\textwidth, alt={}, center]{dd2cb0ec-5df9-4d99-9e15-5ae1f1c07b96-3_490_665_1793_740}
The diagram shows the curve \(y = x ( x - 1 ) ( x - 2 )\), which crosses the \(x\)-axis at the points \(O ( 0,0 )\), \(A ( 1,0 )\) and \(B ( 2,0 )\).
- The tangents to the curve at the points \(A\) and \(B\) meet at the point \(C\). Find the \(x\)-coordinate of \(C\).
- Show by integration that the area of the shaded region \(R _ { 1 }\) is the same as the area of the shaded region \(R _ { 2 }\).