Calculus 10.3 day 2

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10.3 day 2 Calculus of Polar Curves
Lady Bird Johnson Grove, Redwood National Park,
California
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To find the slope of a polar curve
We use the product rule here.
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To find the slope of a polar curve
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Example
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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
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We can use this to find the area inside a polar
graph.
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Example Find the area enclosed by
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Notes
To find the area between curves, subtract
Just like finding the areas between Cartesian
curves, establish limits of integration where the
curves cross.
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When finding area, negative values of r cancel
out
Area of one leaf times 4
Area of four leaves
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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
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There is also a surface area equation similar to
the others we are already familiar with
When rotated about the x-axis
p