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Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 10.3 day 2 Calculus of Polar Curves. Lady Bird Johnson Grove, Redwood National Park, California. Try graphing this on the TI-89. To find the slope of a polar curve:. We use the product rule here.
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Photo by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, Washington 10.3 day 2 Calculus of Polar Curves Lady Bird Johnson Grove, Redwood National Park, California
To find the slope of a polar curve: We use the product rule here.
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:
Notes: To find the area between curves, subtract: Just like finding the areas between Cartesian curves, establish limits of integration where the curves cross.
When finding area, negative values of r cancel out: Area of one leaf times 4: Area of four leaves:
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:
There is also a surface area equation similar to the others we are already familiar with: When rotated about the x-axis: p