Solve the Problem by Integration $y = \frac { 1 } { x ^ { 3 } + 6 x ^ { 2 } + 5 x } , x = 4 , x = 5$

question 315

Multiple Choice

Solve the problem by integration.
-Find the volume generated by rotating the area bounded by $y = \frac { 1 } { x ^ { 3 } + 6 x ^ { 2 } + 5 x } , x = 4 , x = 5$ , and $y = 0$ about the $\mathrm { y }$ -axis.

• A) \(2 \pi \ln \frac { 25 } { 27 }\)
• B) \(\frac { 1 } { 2 } \pi \ln \frac { 3 } { 5 }\)
• C) \(\frac { 1 } { 2 } \pi \ln \frac { 27 } { 25 }\)
• D) \(\frac { 1 } { 4 } \pi \ln \frac { 27 } { 25 }\)

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Definitions:

Respiration

(1) Cellular respiration is the process by which cells generate ATP through a series of redox reactions. In aerobic cellular respiration, the terminal electron acceptor is molecular oxygen; in anaerobic cellular respiration, the terminal acceptor is an inorganic molecule other than oxygen. (2) Organismic respiration is the process of gas exchange between a complex animal and its environment, generally through a specialized respiratory surface, such as a lung or gill.

Calvin Cycle

A series of biochemical reactions taking place in the chloroplasts of photosynthetic organisms, part of the process of converting carbon dioxide and water into glucose, using ATP and NADPH produced in the light reactions of photosynthesis.

Carbon Dioxide Fixation

The process by which inorganic carbon dioxide is converted into organic compounds by living organisms, principally during photosynthesis.

Calvin Cycle

A set of chemical reactions that take place in the chloroplasts of photosynthetic organisms to synthesize glucose from carbon dioxide and water, using ATP and NADPH produced in the light reactions.