$\"\"$

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The function is $\"\"$ and $\"\"$ .

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Area of the region:

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If $\"image\"$ is continuous and non-negative on the closed interval $\"image\"$ ,

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then the area of the region bounded by the graph $\"image\"$ , the $\"image\"$ -axis ( $\"\"$ ) and the vertical lines $\"image\"$ and $\"image\"$ is given by

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$\"\"$

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Area of the bounded region is $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Change of integral limits:

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ and change of limits in $\"\"$ .

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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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$\"\"$ .

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

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$\"\"$

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