Polar Coordinates: Area Formula: Area Between Two Polar Curves

in Threespeak3 months ago (edited)

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In this video I go over a general formula for the area of a region bounded by two polar curves. I illustrated this in an example in my last video on Example 2, but this time go over the general case, as well as some cautionary notes. The area between two polar curves can be determined by subtracting the two areas of each separate polar curves. The only problem we may face is that often times there are many different polar coordinate representations of the exact same point. This means that we can’t simply solve for points that two polar curves intersect at by setting them equal and solving for the other variable, because some points intersect at different “times”. I illustrate this concept by graphing the individual points on the cardioid and circle curves from Example as the angle increases. It is clear that while there are three intersection points, only two of the points occur at exactly the same time. Thus to know that there are three intersection points, it is often helpful to graph both curves, and what better way to graph polar curves than by the amazing Desmos calculator!

This is a very important video to illustrate not only the general formula for determining the area between two polar curves, but also some of the important factors to consider when determining the area, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvVMDuV_c1fa1koBfw

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-area-formula-area-between-two-polar-curves

Related Videos:

Polar Coordinates: Area: Example 2: Cardioid and Circle: https://youtu.be/vSzxzNn3EiA
Polar Coordinates: Area: Example 1: r = cos 2ϴ: https://youtu.be/6kavQyGcODo
Polar Coordinates: Area Formula: https://youtu.be/wd-EwiKzqa0
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .

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