1. Lengths of Curves
7.4

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

3. Example:
Now what? This doesn’t fit any formula, and we started with a pretty simple example!
Use your calculator to integrate

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

5. Example:

6. 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.