$\"\"$

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The function is $\"\"$ .

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Find the volume of the solid by revoving the region about $\"\"$ axis.

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Disk method:

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The volume of the solid of revolution is $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Find the integral by using byparts of integration.

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Integration byparts: $\"\"$ .

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Let $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Apply integral on each side.

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$\"\"$

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Substitute correspnding values in the byparts formula.

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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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Substitute result of $\"\"$ in $\"\"$ .

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$\"\"$

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Aplly integral limits.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Integral converges for $\"\"$ .

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$\"\"$ .