1. Find the length of a curve
This is gonna be GREAT!!!!
AWESOME!!!

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:

3. Lengths of Curves:
We need to get dx out from under the radical.
Length of Curve (Cartesian)

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

5. 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.

6. and by some mathemagic…
Example:
and by some mathemagic…

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.

8. Finding the exact length:
What are these endpoints?

9. Finding the exact length:
Domain
So…..

10. Finding the exact length:

11. Homework!!! Page 567: 3 – 11 odd Ok…#15 and 17 ALRIGHT!!!
Mr. Mitchell is
the greatest
Can we do more?
Ok…#15 and 17