Overview
To study curves which aren't graphs of functions we may parametrize them, identifying a point (x(t), y(t)) that traces a curved path as the value of t changes. We can then use our technique for computing arclength, differential notation, and the chain rule to calculate the length of the parametrized curve over the range of t.
Lecture Video and Notes
Video Excerpts
» Clip 2: Arclength of Parametric Curves (00:05:00)
From Lecture 32 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Arclength of Parametric Curves
> Download from iTunes U (MP4 - 109MB)
> Download from Internet Archive (MP4 - 109MB)
Recitation Video
Parametric Arc Length
> Download from iTunes U (MP4 - 19MB)
> Download from Internet Archive (MP4 - 19MB)
Worked Example
Exploring a Parametric Curve
Lecture Video and Notes
Video Excerpts
» Clip 1: Remarks on Notation (00:05:00)
From Lecture 32 of 18.01 Single Variable Calculus, Fall 2006