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Use the Shell Method to Set Up and Evaluate the Integral

question 87

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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by y=13πex2/3,y=0,x=0y = \frac { 1 } { \sqrt { 3 \pi } } e ^ { - x ^ { 2 } / 3 } , y = 0 , x = 0 , and x=3x = 3 about the yy -axis. Round your answer to three decimal places.

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Definitions:

Achievable

Pertains to goals or objectives that can realistically be accomplished within the available resources and constraints.

Complex

Comprising many interconnected parts or elements; not simple or straightforward, often requiring significant time or effort to understand or deal with.

Direct Observation

A research method where data is collected by watching subjects in their natural or controlled environment without interference or manipulation.

Indirect Observation

Research or data collection method where behavior is observed and recorded without direct interaction with the subjects being studied.

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