$\"\"$

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The curve is $\"\"$ .

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Graph the curve $\"\"$ .

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Shade the required region.

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$\"\"$

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Observe the graph :

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Region enclosed by the given curves is between $\"\"$ and $\"\"$ .

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$\"\"$

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Area enclosed by the curves $\"\"$ and $\"\"$ between $\"\"$ and $\"\"$ is

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$\"\"$ .

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The curve is $\"\"$ .

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$\"\"$

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Top half of the curve is $\"\"$ .

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Observe the graph:

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Curve is symmetrical about $\"\"$ axis,

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Hence the area enclosed by the loop is twice the area of top half of the curve .

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$\"\"$ .

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Assume $\"\"$ .

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$\"\"$ .

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Change of integral limits:

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Lower limt: If $\"\"$ then $\"\"$ .

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Upper limt: If $\"\"$ then $\"\"$ .

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Substitute $\"\"$ and change of limits in $\"\"$ .

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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 is $\"\"$ sq-units.

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$\"\"$

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Area of the region is $\"\"$ sq-units.