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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

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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:

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Example: Now what? This doesn’t fit any formula, and we started with a pretty simple example! The TI-89 gets:

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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:

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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

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Example:

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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

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

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7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington(Photo not taken by Vickie Kelly)

7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington(Photo not taken by Vickie Kelly)

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