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I am aware of the formula.. but can someone give me a clear definition of what the total area enclosed by a polar curve represents. Thanks

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Draw the polar curve on the plane; see the part of it that is "inside"; that's what the "area enclosed by the polar curve" is. –  Arturo Magidin Mar 9 '11 at 5:12
Why does the title say "total area enclosed by a polar curve and the x-axis" and the question "total area enclosed by a polar curve"? Those are two different things. –  joriki Mar 9 '11 at 5:42
If you put together the comments from Arturo and joriki I think you have an answer. If the question is the title and the curve is $r=1$, take the part of the area where $\cos(\theta)\ge 1$. I share their frustration with the conflict. –  Ross Millikan Mar 9 '11 at 6:09

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