$\"\"$

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The function is $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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(a)

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Find $\"\"$ - axis: Solve the function in terms of $\"\"$ .

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By usig shell method $\"\"$

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Integrate with $\"\"$ to $\"\"$ .

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$\"\"$

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Power rule of integral is $\"\"$

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$\"\"$

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The volume of the curve about $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(b)

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Find $\"\"$ - axis:

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Solve the function in terms of $\"\"$ .

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Integrate with $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The volume of the curve about $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(c)

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\

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Find $\"\"$ :

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Solve the function in terms of $\"\"$ .

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The radius of the curve is $\"\"$

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The height of the curve is $\"\"$

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By usig shell method.

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Integrate with $\"\"$ to $\"\"$ .

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$\"\"$

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Power rule of integral is $\"\"$

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$\"\"$

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The volume of the curve is $\"\"$ .

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$\"\"$

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Graph:

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

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$\"\"$

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Observe the graph,

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The intersection points are $\"\"$ and $\"\"$ the region is bounded.

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$\"\"$

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(a) The volume of the curve about $\"\"$ -axis is $\"\"$

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(b) The volume of the curve about $\"\"$ -axis is $\"\"$ .

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(c) The volume of the curve is $\"\"$ .