Arc Length Parameterization | Calculus 3 Lesson 31 - JK Math

How to Find Arc Length Functions & Reparameterize Vector Functions (Calculus 3 Lesson 31) ➡️ Download my FREE Surfaces Cheat Sheets: https://www.jkmathematics.com/surfaces-cheat-sheets 🖥️ Membership Site (community & bonus content): https://www.jkmathematics.com/plus 🌐 My Website: https://www.jkmathematics.com ⭐️ Support Me on Patreon: https://www.patreon.com/JKMath 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: https://youtu.be/N2A5wBmyi-U ⏩ Next Lesson: https://youtu.be/BYJFf-MQuqA 📺 Calculus 3 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE5yZ7ydR9qeB_B6CcVFlX63 📺 Calculus 2 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 Algebra: https://amzn.to/3Eaq1cy ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Follow me on Social Media! https://www.facebook.com/jkmathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! - Josh from JK Mathematics #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.