Step 1 :

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The triple integral is $\"\"$

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Conversion from rectangular to cylindrical co-ordinates :

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$\"\"$

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Conversion of integral from rectangular to cylindrical co-ordinates :

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$\"\"$

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Here $\"\"$ .

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Substitute $\"\"$ in above equation.

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The triple integral function in cylindrical co-ordinates is $\"\"$ .

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Find the z limits :

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Upper limit: If $\"\"$ , then $\"\"$

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Lower limit: If $\"\"$ , then $\"\"$ .

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Find the r and $\"\"$ limits :

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Consider $\"\"$ .

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If $\"\"$ then,

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$\"\"$

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As $\"\"$ ranges from $\"\"$ to $\"\"$ and $\"\"$ ranges from $\"\"$ to $\"\"$ .

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This forms a circle with radius $\"\"$ ,

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In cylindrical coordinates , we can write radius ranges from $\"\"$ to $\"\"$ and $\"\"$ rages from $\"\"$ to $\"\"$ .

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Therefore the double integral can be written as $\"\"$ .

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$\"\"$

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Substitute integral limits and $\"\"$ in above formula

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$\"\"$

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Integral formula: $\"\"$

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$\"\"$

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Step 2 :

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Conversion from rectangular to spherical co-ordinates :

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$\"\"$

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Conversion of integral from rectangular to cylindrical co-ordinates :

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$\"\"$

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