$\"\"$

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The center of mass of the plate (or the centroid of $\"\"$ ) is located at the point $\"\"$ , where

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

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$\"\"$

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$\"\"$ is the $\"\"$ -coordinate of the centroid of the region that lies under the graph of a continuous function $\"\"$ , where $\"\"$ .

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Show that $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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Multiply each side by constant $\"\"$ .

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$\"\"$

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Add $\"\"$ to each side.

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$\"\"$

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$\"\"$

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$\"\"$ .