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How to Find the Arc Length of Space Curves (Calculus 3 Lesson 30)

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In this video you will learn how to find the arc length of space curves by integrating the magnitude of the derivative of the vector-valued function that represents the curve. We extend the arc length formula from 2D to 3D, redefine it using vector functions, and then practice using the formula with example problems.

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 Extending Formula from 2D to 3D
6:42 Arc Length Formula
7:32 Example: 〈3cos(t), 4t, 3sin(t)〉on [0,4π]
13:59 Example: 〈e^t*sin(t), 2e^t, e^t*cos(t)〉on [0,π]


📝 Examples Video:    • Arc Length of Space Curves Examples | Calc...  

⏩ Next Lesson:    • Arc Length Parameterization | Calculus 3 L...  

📺 Calculus 3 Playlist:    • Calculus 3  

📺 Calculus 2 Playlist:    • Calculus 2  

📺 Calculus 1 Playlist:    • Calculus 1  


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Josh from JK Mathematics

#calculus

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