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) \(2 \pi \left( e ^ { 10 } - e ^ { 2 } \right)\)

Describe the biosphere and its significance.

Comprehend the concepts of exponential growth, carrying capacity, and environmental resistance.

Recognize patterns of population growth and demographic transitions.

Understand the factors that contribute to environmental resistance.

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