$\"\"$

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The equations are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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Consider $\"\"$ and $\"\"$ .

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Area of the region:

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If $\"\"$ and $\"\"$ are continuous on $\"\"$ and $\"\"$ for all $\"\"$ in $\"\"$ , then the area of the region bounded by the graphs of $\"\"$ and $\"\"$ and the vertical lines $\"\"$ and $\"\"$ is $\"\"$ .

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Graph the equations $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph:

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Area of the region bounded by $\"\"$ and $\"\"$ is from $\"\"$ to $\"\"$ .

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The two curves are symmetric about $\"\"$ -axis and $\"\"$ on interval $\"\"$ .

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The area enclosed by the curves is $\"\"$ .

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$\"\"$

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Consider integrand $\"\"$

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$\"\"$

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Partial decomposition:

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$\"\"$

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Substitute $\"\"$ in the expression (2).

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$\"\"$

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Substitute $\"\"$ in the expression (2).

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in (1).

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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