Arc Length

From Department of Mathematics at UTSA
Revision as of 10:15, 2 November 2021 by Lila (talk | contribs) (→‎Resources)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

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: