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10.6: The Calculus of Polar Curves

Try graphing this on the TI-89. 10.6: The Calculus of Polar Curves. Greg Kelly, Hanford High School, Richland, Washington. To find the slope of a polar curve:. We use the product rule here. To find the slope of a polar curve:. Example:. Area Inside a Polar Graph:.

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10.6: The Calculus of Polar Curves

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  1. Try graphing this on the TI-89. 10.6: The Calculus of Polar Curves Greg Kelly, Hanford High School, Richland, Washington

  2. To find the slope of a polar curve: We use the product rule here.

  3. To find the slope of a polar curve:

  4. Example:

  5. Area Inside a Polar Graph: The length of an arc (in a circle) is given by r.q when q is given in radians. For a very small q, the curve could be approximated by a straight line and the area could be found using the triangle formula:

  6. We can use this to find the area inside a polar graph.

  7. Example: Find the area enclosed by:

  8. Notes: To find the area between curves, subtract: Just like finding the areas between Cartesian curves, establish limits of integration where the curves cross.

  9. When finding area, negative values of r cancel out: Area of one leaf times 4: Area of four leaves:

  10. To find the length of a curve: Remember: For polar graphs: If we find derivatives and plug them into the formula, we (eventually) get: So:

  11. There is also a surface area equation similar to the others we are already familiar with: When rotated about the x-axis: p

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