Find the Volume of the Solid Obtained by Rotating the Region

question 21

Multiple Choice

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
$y = \ln x , y = 1 , y = 5 , x = 0$ ; about the $y$ - axis

• A) \(\frac { \pi } { 4 } \left( e ^ { 10 } - e \right)\)
• B) \(\frac { \pi } { 2 } \left( 1 - e ^ { 10 } \right)\)
• C) \(\frac { \pi } { 2 } \left( e ^ { 10 } - e ^ { 2 } \right)\)
• D) \(\frac { \pi e ^ { 10 } } { 2 }\)
• E) \(2 \pi \left( e ^ { 10 } - e ^ { 2 } \right)\)

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Definitions:

Hysterical Personality Disorder

An outdated term that was once used to describe a pattern of dramatic and attention-seeking behavior, now more accurately referred to as histrionic personality disorder.

Emotionally Charged

Refers to situations, events, or topics that evoke strong emotional responses.

Interpersonal Problems

Difficulties in interaction and communication between individuals that may lead to conflict or emotional stress.

Schizotypal Personality Disorder

A psychiatric disorder defined by extreme fear in social situations, impaired reasoning, paranoid thoughts, a sense of being detached from the environment, short-term psychosis, and often peculiar beliefs.