Use the Shell Method to Find the Volume of the Solid

question 46

Multiple Choice

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and
lines about the x-axis.
- $$x = 4 e ^ { - y ^ { 2 } } , y = 0 , x = 0 , y = 1$$

• A) \(8 \left( 1 + \frac { 1 } { \mathrm { e } } \right) \pi\)
• B) \(4 ( e - 1 ) \pi\)
• C) \(4 \left( 1 - \frac { 1 } { \mathrm { e } } \right) \pi\)
• D) \(8 \left( 1 - \frac { 1 } { \mathrm { e } } \right) \pi\)

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Definitions:

Predictive Statistics

Predictive statistics involves using historical data to make predictions about future events, often employing models and algorithms to forecast trends and outcomes.

Historical Data

Information or records relating to past events, conditions, or performances, used for analysis, comparison, or forecasting.

Sample

A subset of a population selected for measurement, observation, or questioning to provide statistical information about the population.

Population

The entire group of individuals or items that is the subject of a statistical analysis.