In this video I go further into determining the area of polar curves and this time do an example on evaluating the area of one loop of a 4 leaved rose given by the polar curve y = cos 2ϴ. I had graphed this curve in my Example 8 video, and I use the fact that one of the loops is bounded by the angles -π/4 and π/4. Thus we can apply the formula for area I derived in my last video, or remember the fact that the formula was derived by summing up an infinite amount of sectors of a circle, which we know the formula for as ½r2ϴ. I also use symmetry to simplify the resulting integral and show that the area of one of the loops is π/8, thus the full curve is four times that, π/2. This is a very useful video in applying the area formula for polar curves so make sure to watch this video!
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Polar Coordinates: Area: Example 1: r = cos 2ϴ
Example: Find the area enclosed by one loop of the four-leaved rose r = cos 2θ.