$\"\"$

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The curves are $\"\"$ .

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Graph the curves on the same graph.

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$\"\"$

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Observe the graph :

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The curve intersects at $\"\"$ and $\"\"$ .

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The pink color represents the curve $\"\"$ .

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The green color represents the curve $\"\"$ .

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The red color represents the curve $\"\"$ .

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

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

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Centeriod is given by $\"\"$ .

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$\"\"$

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The boundary of the region is in $\"\"$ interval $\"\"$ .

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The integral is carried peicewise because in the interval $\"\"$ is bounded by $\"\"$ and $\"\"$ below.

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The interval $\"\"$ is bounded by $\"\"$ above and $\"\"$ below.

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

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$\"\"$

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$\"\"$

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The formula for $\"\"$ .

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Subustiute the values in the formula.

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$\"\"$

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$\"\"$

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The formula for $\"\"$ .

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Subustiute the values in the formula.

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$\"\"$

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Now calculate the points of the centeriod $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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

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The graph of the functions $\"\"$ with the centeroid $\"\"$ .

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$\"\"$ .