Sec. 7.4: Lengths of Curves. HOW CAN WE FIND THE EXACT LENGTH OF THE CURVE??

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Presentation transcript:

Sec. 7.4: Lengths of Curves

HOW CAN WE FIND THE EXACT LENGTH OF THE CURVE??

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:

Now what? This doesn’t fit any formula, and we started with a pretty simple example! Use your calculator to get the final answer!

Example: Bill is writing an estimate for his construction company to be chosen as the company that will build a new road in his town. The road is shown below. The road is 24 feet wide and must be paved 3 inches thick. Bill charges $75 per cubic yard of asphalt. What amount should he give the local government as an estimate of the cost of this project?