Find the Volume of the Solid Obtained by Rotating the Region

question 7

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:

Convincing Evidence

Evidence that is robust and compelling enough to persuade an individual to accept its validity or truth.

Testable Prediction

A statement that can be verified through experimentation or observation, often forming the basis of a scientific hypothesis.

Independent Variables

In experimentation, a variable that is manipulated to determine if it causes a change in another variable.

Falsifiable

A characteristic of a statement, hypothesis, or theory that allows it to be proven false by an observation or experiment.