1)

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Step 1:

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The curve is $\"\"$ .

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Graph the curve $\"\"$ . \ \

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$\"\"$

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Determine the area below the curve and above the $\"\"$ axis. \ \

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Observe the graph:

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The points of intersection are $\"\"$ and $\"\"$ .

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Definite integral as area of the region:

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If $\"image\"$ and $\"image\"$ are continuous and non-negative on the closed interval $\"image\"$ ,then the area of the region bounded by the graphs of $\"image\"$ and $\"image\"$ and the vertical lines $\"image\"$ and $\"image\"$ is given by

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$\"image\"$ .

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

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Integral limits are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Apply power rule of integration: $\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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2)

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The curve is $\"\"$ .

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Graph the curve $\"\"$ . \ \

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$\"\"$

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Determine the area right of the curve and left of the $\"\"$ axis. \ \

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Observe the graph:

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The points of intersection are $\"\"$ and $\"\"$ .

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Definite integral as area of the region:

\

If $\"image\"$ and $\"image\"$ are continuous and non-negative on the closed interval $\"image\"$ ,then the area of the region bounded by the graphs of $\"image\"$ and $\"image\"$ and the vertical lines $\"\"$ and $\"\"$ is given by

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$\"\"$ , $\"\"$ .

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

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Integral limits are $\"\"$ and $\"\"$ .

\

$\"\"$

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$\"\"$

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$\"\"$

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Apply power rule of integration: $\"image\"$ .

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$\"\"$

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$\"\"$ \ \

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$\"\"$

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$\"\"$ .

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