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 polar curve  $r=f(\theta )$  with  $\alpha _{1}\leq \theta \leq \alpha _{2}$  is
$L=\int _{\alpha _{1}}^{\alpha _{2}}{\sqrt {r^{2}+{\bigg (}{\frac {dr}{d\theta }}{\bigg )}^{2}}}d\theta .$

Solution:

Step 1:

Step 2:

Final Answer:

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