$\"\"$

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The functions are $\"\"$ and $\"\"$ .

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The interval is $\"\"$ .

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The region bounded by the curves :

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$\"\"$

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Graphically, the area of the region bounded by the curves $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$

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The centroid is $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Integration by parts :

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Solve the integral by using parts of integration method.

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Formula for integration by parts : $\"\"$ .

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

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply integral on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute the corresponding values in $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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The $\"\"$ -coordinate of the centroid is $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in above equation.

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$\"\"$ .

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$\"\"$ .

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From power reducing formula : $\"\"$ .

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$\"\"$

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The $\"\"$ -coordinate centroid is $\"\"$ .

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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 $\"\"$ and $\"\"$ with the centeroid $\"\"$

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$\"\"$