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The area (in square units) of the region bounded by the curves $2x=y^2-1$ and $x=0$ is

\[\begin {array} {1 1} (1)\;\frac{1}{3} & \quad (2)\;\frac{2}{3} \\ (3)\;1 & \quad (4)\;2 \end {array}\]

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$(2) \frac{2}{3}$
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