2018 TGM P2 Q2

The diagram shows the curve \(C\) with equation \(y^2 = 2x\sqrt{4 - x^2}\). The region enclosed by \(C\) is denoted by \(R\).

1. Write down an integral that gives the area of \(R\), and evaluate this integral numerically.[3]
2. The part \(R\) above the \(x\)-axis is rotated through \(2\pi\) radians about \(x\)-axis. Find the exact value of the volume obtained.[3]
3. Find the exact \(x\)-coordinate of the maximum point of \(C\).[3]