009C Sample Final 2, Problem 10

Find the length of the curve given by

$x=t^{2}$

$y=t^{3}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:

Return to Sample Exam