$\"\"$

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The curve equation is $\"\"$ .

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Graph the equation $\"\"$ .

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$\"\"$

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Observe the graph:

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The first half of the curve lies between $\"\"$ .

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$\"\"$

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Area of the region enclosed by the curve is $\"\"$ .

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The boundaries of the half of the curve are $\"\"$ and $\"\"$ .

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Area of the region enclosed by the curve $\"\"$ :

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Area of the region enclosed by loop of the curve is $\"\"$ . $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Area of the region enclosed by one loop of the curve is $\"\"$ .

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$\"\"$

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Area of the region enclosed by one loop of the curve is $\"\"$ .