8.4: Lengths of Curves
- In this subunit, we will make use of another concept that you have known and understood for quite some time: the distance formula. If you want to estimate the length of a curve on a certain interval, you can simply calculate the distance between the initial point and terminal point using the traditional formula. If you want to increase the accuracy of this measurement, you can identify a third point in the middle and calculate the sum of the two resulting distances. As we add more points to the formula, our accuracy increases: the exact length of the curve will be the sum (i.e. the integral) of the infinitesimally small distances.
- University of Wisconsin H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.3: Length of a Curve" URL
  Read Section 6.3 (pages 319 through 325). This reading discusses how to calculate the length of a curve, also known as arc length. This includes calculating arc length for parametrically-defined curves.
- Massachusetts Institute of Technology: David Jerison's "Parametric Equations, Arclength, Surface Area" Page
  Watch this lecture until 26:10. Lecture notes are available in PDF; the link is on the same page as the lecture.
- Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web" URL
  Click on the "Index" for Book II. Scroll down to "2. Applications of Integration," and click button 125 (Arc Length). Work on all of the problems (1-9). If at any time a problem set seems too easy for you, feel free to move on.

8.4: Lengths of Curves