(Unit 2 Lecture 7) For a smoothly parametrized curve r(t), we introduce arc length and the arc length We start by understanding arclength as the distance a curve travels. Two examples are provided to illustrate the calculation of arclength: the unit circle and a more complex parametric curve.
We then introduce the arclength function, which generalizes the concept of arclength to any point along the curve. The lecture concludes by applying the Fundamental Theorem of Calculus to understand the relationship between the arclength function and the speed of the curve.
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