The area of the region lying in the first quadrant and bounded by the curve $y = 4x^2$, the $Y$-axis, and the lines $y = 2$ and $y = 4$ is:
- A$\frac{1}{3}[8 - 2\sqrt{2}]$ sq. units
- B$\frac{1}{3}[8 + 2\sqrt{2}]$ sq. units
- C$\frac{1}{2}[8 - 2\sqrt{2}]$ sq. units
- D$\frac{1}{2}[8 + 2\sqrt{2}]$ sq. units
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