Mathematics: Arc Length of a Curve as an Application of Integration

Topic: Arc length of a curve as an Application of Integration
Discipline(s) or Field(s): Mathematics
Authors: Kavita Bhatia, University of Wisconsin-Marshfield/Wood County & Kirthi Premadasa, UW-Marathon County
Submission Date: March 30, 2010

Lesson Goals:

  1. Students will learn how to make a manual calculation of a Riemann sum for the arc length of a givensample curve using a few subdivisions.
  2. Students will use the knowledge obtained through the Riemann Sum ‐> Integrations models that they have seen before, to “discover” an integration formula for the arc length of any continuous curve.
  3. Students will use the formula that they “discovered”, together with the integration techniques, taught in the course to evaluate the actual arc length of the curve.
  4. Students will understand the underlying theme behind all the Riemann sums that they have encountered.

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