Find the Length of a Loop of a Curve Given by Parametric Equations

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This video provides an example of how to determine the arc length of a loop of a plane curve given by parametric equations.
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You explained this very clearly. Thanks for posting such a helpful video. Helped me solve a problem I was stuck on for quite some time. :)

alext
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How to find out the upper and lower boundary for t if the graph is not known?

GongShangyu
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I'm graphing this on my Ti Nspire and it is not giving me the full loop (it looks like the top half of a parabola). Any idea on what I'm doing wrong.

zagacks