Course: Calculus II
Topic: Geometry
Subtopic: Arc Length


In this lesson we will use definite integrals to find the length of an arc, that is, the length of a portion of a curve. If the curve is a regular shape, such as an ellipse, then we have a formula to find its perimeter. However, if the curve is irregular then calculus is needed to find its length. The plan will be, as usual, to find the length of a tiny piece of the curve then add the little lengths up to get the arc length.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: arc of a curve, central angle, subtends (as in "the angle subtends the arc")

Mini-Lectures and Examples

STUDY: Geometry - Arc Length of Curve

Supplemental Resources (optional)

Video: Arc Length and Surface Area, Selwyn Hollis's Video Calculus (watch 1st half)

Lesson: Arc Length, Paul's Online Notes for Calc II

PDF: Lengths of Curves and Areas of Surfaces of Revolution, Dale Hoffman's Contemporary Calculus (study arc length sections)

Desmos Exploration: Arc Length

rev. 2021-01-09