Session 78: Computing the Length of a Curve

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Overview

To find the length of a curve we break it up into infinitesimal pieces. Each piece is approximately a straight line segment; we use differential notation to compute and sum the lengths of these pieces.

Lecture Video and Notes

Video Excerpts

» Clip 1: Introduction to Arc Length (00:09:00)

» Accompanying Notes (PDF)

From Lecture 31 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Example: y=mx (00:03:00)

» Accompanying Notes (PDF)

From Lecture 31 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Example: Circular Arc (00:07:00)

» Accompanying Notes (PDF)

From Lecture 31 of 18.01 Single Variable Calculus, Fall 2006

» Clip 4: Example: Length of a Parabola (00:06:00)

» Accompanying Notes (PDF)

From Lecture 31 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Arc Length of y=x3/2

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> Download from iTunes U (MP4 - 15MB)

> Download from Internet Archive (MP4 - 15MB)

> Download English-US transcript (PDF)

> Download English-US caption (SRT)

Worked Example

 

Arc Length of y=ln(x)

 

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