10.6: The Calculus of Polar Curves

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Presentation transcript:

10.6: The Calculus of Polar Curves Try graphing this on the TI-89. 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: 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:

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

Example: Find the area enclosed by:

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