The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:
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The area bounded by the parabola $y^2 = 4ax$ and the line $y = mx$ is given by the direct formula $\frac{8a^2}{3m^3}$. Here, $4a = 4 \implies a = 1$ and $m = 2$, so $\frac{8(1)^2}{3(2)^3} = \frac{8}{24} = \frac{1}{3}$.