Arc Length Parameterization | Calculus 3 Lesson 31 - JK Math
How to Find Arc Length Functions & Reparameterize Vector Functions (Calculus 3 Lesson 31)
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In this video you will learn how to find the arc length function for a space curve and then use it to reparameterize the space curve in terms of the arc length parameter.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 What is the Arc Length Parameter?
6:02 Arc Length Function Formula
7:34 Example Part 1: Finding an Arc Length Function
12:05 Example Part 2: Reparameterization
16:06 Example Part 3: Unit Tangent Vector?
20:08 Summary of Arc Length Parameterization
21:45 Final Example: 〈3t²+1, t²-4, 5t²〉on [1,10]
Corrections:
30:05 I forgot to add 1 when rewriting this component. The original component was 3t^2+1, so after replacing t^2 when reparameterizing, you should have (3s/√35+4)î for the x component. My apologies on this mistake!
📝 Examples Video: • Arc Length Parameterization Examples | Cal...
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Josh from JK Mathematics
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