**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:*

- 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.
- 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.
- 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.
- Students will understand the underlying theme behind all the Riemann sums that they have encountered.

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