Finding Arc Lengths of Curves Given by Parametric Equations
Abigail Young
6 min read
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Study Guide Overview
This study guide covers finding arc lengths of parametric curves, an AP Calculus BC topic. It reviews the concept of arc length and its formula derivation for Cartesian equations. It then explains the relationship between parametric and Cartesian equations and derives the arc length formula for parametric curves. Finally, it provides practice problems demonstrating the application of this formula.
#9.3 Finding Arc Lengths of Curves Given by Parametric Equations
For this portion of the AP Calculus BC course, we will learn how to apply what we have previously learned about arc length to parametric curves. To learn more about finding arc lengths of smooth planar curves, please refer to the Unit 8.13 study guide!
#🏹 Reviewing Arc Length
In calculus, the arc length of a curve refers to the distance between two points on a curve. For example, if we were to mark two points on a paperclip, we could measure the arc length between those two points by unraveling the paperclip. Once the paperclip is straightened out, we can use a ruler to measure the distance between those two points. A similar strategy is used to measure the arc length of a curve.
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Visualization of Arc Length Formula
Image Courtesy of Math Is Fun
#✏️ Derivation of Arc Length Formula (Cartesian)
This image above depicts how calculus can be used to calculate the arc l...
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