Difference between revisions of "Arc Length"

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==Resources==
 
==Resources==
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* [https://en.wikibooks.org/wiki/Calculus/Arc_length Arc Length], WikiBooks: Calculus
 
* [https://openstax.org/books/calculus-volume-3/pages/3-3-arc-length-and-curvature Arc Length and Curvature], OpenStax
 
* [https://openstax.org/books/calculus-volume-3/pages/3-3-arc-length-and-curvature Arc Length and Curvature], OpenStax
 +
 +
==Licensing==
 +
Content obtained and/or adapted from:
 +
* [https://en.wikibooks.org/wiki/Calculus/Arc_length Arc Length, WikiBooks: Calculus] under a CC BY-SA license

Latest revision as of 10:15, 2 November 2021

We can deduce that the length of a curve with parametric equations , should be:

Since vector functions are fundamentally parametric equations with directions, we can utilize the formula above into the length of a space curve.

Arc length of a space curve

If the curve has the vector equation , or, equivalently, the parametric equations , where are continuous, then the length of the curve from to is:

}}

For those who prefer simplicity, the formula can be rewritten into:

or

Example Problems

1. Find the circumference of the circle given by the parametric equations , with .

2. Find the length of the curve from to .

Resources

Licensing

Content obtained and/or adapted from: