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
Greg Kelly, Hanford High School, Richland, Washington
We use the product rule here.
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:
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:
For polar graphs:
If we find derivatives and plug them into the formula, we (eventually) get:
There is also a surface area equation similar to the others we are already familiar with:
When rotated about the x-axis: