$\"\"$

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The centroid of the ellipse:

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The $\"\"$ -coordinate of the centre of mass is $\"\"$ .

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The $\"\"$ -coordinate of the centre of mass is $\"\"$ .

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Consider a region bounded by $\"\"$ and $\"\"$ -axis in the interval $\"\"$ .

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The area of the region is $\"\"$ .

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$\"\"$

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The ellipse equation is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The top half of the ellipse is $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Apply the 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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The $\"\"$ -coordinate of the centre of mass is $\"\"$ since the Centriod of the region bounded by the $\"\"$ -axis .

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Hence $\"\"$ .

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The $\"\"$ -coordinate of the centre of mass is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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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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The centroid of the region enclosed by the $\"\"$ -axis of the ellipse is $\"\"$ .

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$\"\"$

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The centroid of the region enclosed by the $\"\"$ -axis of the ellipse is $\"\"$ .