MATH 211 Lecture Notes - Lecture 12: Cartesian Coordinate System, Curve, Parametric Equation

• School: BRCC
• Department: MATH - Mathematics
• Course: MATH 211
• Professor: William F.Bertolette

Document Summary

Math 212 section 12. 5 arc length and curvature. Recall from section 10. 3, the arc length of a smooth plane curve c given by the parametric equation and , where a t b is [ ] [ ] Now, writing c as the vector valued function. We have the arc length . Now we have the tools to extend the formula of arc length to a curve in space. Example 1: finding arc length of a curve in space. Find the arc length of the curve given by from t = 0 to t = 2. Example 2: finding the arc length of a helix. Find the length of one turn of the helix given by . For motion along the curve, the convenient parameter is time t. for studying geometric properties of a curve, the convenient parameter is arc length s. Note that the arc length function is nonnegative.