2011 CJC P1 Q8

The diagram below shows the curve with equation \(y={{x}^{2}}-1\), \(x>0\) and the tangent \(y=2x-2\) to the curve at the point \((1,0)\).

1. Write down the coordinates of the point where this tangent meets the line \(x=3\).[1]

The region, \(R\), shaded in the diagram, is bounded by the curve, the tangent to the curve at \((1,0)\) and the line \(x=3\).

Find

2. the area of \(R\),[2]
3. the exact volume of the solid of revolution obtained when \(R\) is rotated through \(2\pi \) radians about the \(y\)-axis.[4]