Find the length of the curve given by  in 

To find the length of the curve given by the parametric equations \( x = t^2 \) and \( y = 2t^2 \) for \( 0 \leq t \leq 2 \), we use the arc length formula for parametric curves:

\[
L = \int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt
\]

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