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:

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Sterile Catheter

A medical device used to drain fluids from or administer fluids to the body, sterilized to eliminate any microbes and minimize the risk of infection.