(a)

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Step 1 :

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The graphs of the equations are $\"\"$ .

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Sketch the region bounded graphs :

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Graph the functions $\"\"$ and $\"\"$ .

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Shade the region bounded by the curves between $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph for intersection points are $\"\"$ and $\"\"$ .

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Solution:

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Regions bounded by the graphs of equations is

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$\"\"$

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(b)

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Step 1 :

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The graphs of the equations are $\"\"$ .

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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 $\"image\"$ ,

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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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$\"\"$ .

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The area of the region bounded by the curves contains 3 sub regions as shown below.

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$\"\"$

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Region R₁ :

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$\"\"$

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Upper curve : $\"\"$ .

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Lower curve : $\"\"$ .

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Region R₂ :

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$\"\"$

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Upper curve : $\"\"$ .

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Lower curve : $\"\"$ .

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Region R₃ :

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$\"\"$

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Upper curve : $\"\"$ .

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Lower curve : $\"\"$ .

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Area bounded by the curves :

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$\"\"$

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$\"\"$

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The area bounded by the region is $\"\"$ square units.

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