$\"\"$

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The functions are $\"\"$ and $\"\"$ . (a)

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Graph :

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

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$\"\"$ \ \

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Observe the graph :

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

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$\"\"$

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(b)

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Evaluate the integrals $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, $\"\"$ and $\"\"$ .

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$\"\"$

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(c)

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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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The area between the two curves $\"\"$ and $\"\"$ is $\"\"$ .

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substitute $\"\"$ and $\"\"$ .

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$\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$

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(d)

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The functions are $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Evaluate $\"\"$ .

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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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(e)

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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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(a)

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Graph :

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

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$\"\"$

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Observe the graph :

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

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(b) $\"\"$ and $\"\"$ .

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(c) $\"\"$ .

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(d) $\"\"$ .

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(e) 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 $\"\"$ .