$\"\"$

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The curves are $\"\"$ and $\"\"$ .

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Find area of the region.

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Area is region enclosed by the astroid equal to $\"\"$ into area of the region in the first quadrant.

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Area is region below the curve and above the $\"\"$ - axis is $\"\"$ .

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The curve is $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Change of integral limits:

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$\"\"$ then $\"\"$ .

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$\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ and limits $\"\"$ in the area formula.

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$\"\"$

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$\"\"$

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$\"\"$

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Integral reduction formula: $\"\"$

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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 is enclosed by the astroid is $\"\"$ .

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$\"\"$

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Area is enclosed by the astroid $\"\"$ is $\"\"$ .