$\"\"$

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(a)

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

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

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Shade the region between the curves.

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$\"\"$

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Observe the graph:

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The upper curve is $\"\"$ and lower curve is $\"\"$ on $\"\"$ .

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$\"\"$

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(b)

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Area of the region:

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

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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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 region is $\"\"$ .

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$\"\"$

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(c)

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Estimate the area by using graph:

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$\"\"$

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Observe the graph:

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

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$\"\"$

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(a) Graph:

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$\"\"$

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(b) The area of the region is $\"\"$ .