1. Golden Spike National Historic Site, Promontory, Utah Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999 7.4 Day 1 Lengths of Curves

2. If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical. Length of Curve (Cartesian)Lengths of Curves:

3. Example: Now what? This doesn’t fit any formula, and we started with a pretty simple example! Graphing Calculator

4. Example: The curve should be a little longer than the straight line, so our answer seems reasonable. If we check the length of a straight line:

5. Example: Fill in the information and integrate: