Solve the Problem $x$ -Axis, the Curve $y = \sqrt { \frac { 5 x } { x ^ { 2 } + 1 } } , x = 1$

question 22

Multiple Choice

Solve the problem.
-Find the volume of the solid that is generated by revolving the area bounded by the $x$ -axis, the curve $y = \sqrt { \frac { 5 x } { x ^ { 2 } + 1 } } , x = 1$ , and $x = 3$ about the $x$ -axis.

• A) \(\frac { 5 } { 4 } \pi \ln \left( \frac { 1 } { 5 } \right)\)
• B) \(\frac { 5 } { 2 } \pi \ln ( 5 )\)
• C) \(\frac { 5 } { 2 } \ln ( 5 )\)
• D) \(5 \pi \ln \left( \frac { 1 } { 5 } \right)\)

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Definitions:

Service Factor

A multiplier used in engineering and operations management to account for potential variability in demand or capacity, ensuring systems can handle peak loads.

Violate

To break or fail to comply with a rule or formal agreement.

Multichannel, Multiphase System

A system that involves multiple pathways and stages through which a process or service is completed, often used in reference to service systems with different phases of customer interaction.