The area (in sq.units) of the region

Question:

The area (in sq.units) of the region $\left\{(x, y): y^{2} \geq 2 x\right.$ and $\left.x^{2}+y^{2} \leq 4 x, x \geq 0, y \geq 0\right\}$ is :-

  1. $\frac{\pi}{2}-\frac{2 \sqrt{2}}{3}$

  2. $\pi-\frac{4}{3}$

  3. $\pi-\frac{8}{3}$

  4. $\pi-\frac{4 \sqrt{2}}{3}$


Correct Option: , 3

Solution:

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