$\"\"$

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(a)

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

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

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$\"\"$

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Graph the curves $\"\"$ , $\"\"$ and $\"\"$ .

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Shade the region between the curves.

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$\"\"$

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Note : The region indicated in green color is the region bounded by the three curves.

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

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Observe the graph :

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The region is bounded between $\"\"$ to $\"\"$ .

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Area of the region is $\"\"$

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$\"\"$ .

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It is difficult to evaluate the integral since it does not have any elementary antiderivative.

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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 $\"\"$ sq-units.

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$\"\"$

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(a)

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Graph the curves $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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(b) $\"\"$ .

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It is difficult to evaluate the integral since it does not have any elementary antiderivative.

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(c) The area of the region is $\"\"$ sq-units.