Area with Polar Coordinates

Area with Polar Coordinates - Area with Polar Coordinates...

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Area with Polar Coordinates In this section we are going to look at areas enclosed by polar curves. Note as well that we said “enclosed by” instead of “under” as we typically have in these problems. These problems work a little differently in polar coordinates. Here is a sketch of what the area that we’ll be finding in this section looks like. We’ll be looking for the shaded area in the sketch above. The formula for finding this area is, Notice that we use r in the integral instead of so make sure and substitute accordingly when doing the integral. Let’s take a look at an example. Example 1 Determine the area of the inner loop of . Solution We graphed this function back when we first started looking at polar coordinates . For this problem we’ll also need to know the values of where the curve goes through the origin. We can get these by setting the equation equal to zero and solving.
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Can you see why we needed to know the values of where the curve goes through the origin? These points define where the inner loop starts and ends and hence are also the limits of integration in the formula. So, the area is then,
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This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.

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Area with Polar Coordinates - Area with Polar Coordinates...

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