$\"\"$

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The function are $\"\"$ , $\"\"$ and $\"\"$

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The region bounded by the curves :

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$\"\"$

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Observe the graph,

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The area of the region bounded by the curves is $\"\"$ .

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

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$\"\"$

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Find area of the region. \ \

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$\"\"$

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Power rule of integral : $\"\"$ .

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$\"\"$

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$\"\"$

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The centroid is $\"\"$ . \ \

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Find $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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Power rule of integral : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

\

$\"\"$

\

Power rule of integral : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

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

\

$\"\"$

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