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! The TI-89 gets:

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: You may want to let the calculator find the derivative too: Important: You must delete the variable y when you are done! ENTER F44 Y STO Y

6. Example:

7. If you have an equation that is easier to solve for x than for y, the length of the curve can be found the same way. Notice that x and y are reversed. ENTER X STO

8. Don’t forget to clear the x and y variables when you are done! ENTER F44 Y X 