009C Sample Final 2, Problem 10

Find the length of the curve given by

$x=t^{2}$

$y=t^{3}$

$0\leq t\leq 2$

Foundations:
The formula for the arc length  $L$  of a parametric curve with  $\alpha \leq t\leq \beta$  is
$L=\int _{\alpha }^{\beta }{\sqrt {{\bigg (}{\frac {dx}{dt}}{\bigg )}^{2}+{\bigg (}{\frac {dy}{dt}}{\bigg )}^{2}}}~dt.$

Solution:

Step 1:

Step 2:

Final Answer:

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