Solve the Problem $y = e ^ { - 2 x }$

question 91

Multiple Choice

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve $y = e ^ { - 2 x }$ , and the line $x = 6$ about the $y$ -axis.

• A) \(\frac { 1 } { 2 } \pi \left( 1 - 13 \mathrm { e } ^ { - 12 } \right)\)
• B) \(- \frac { 1 } { 2 } \pi \left( 1 + 13 \mathrm { e } ^ { - 12 } \right)\)
• C) \(\frac { 1 } { 2 } \pi \left( 1 - 11 \mathrm { e } ^ { - 12 } \right)\)
• D) \(\frac { 1 } { 2 } \pi \left( 1 - 12 \mathrm { e } ^ { - 12 } \right)\)

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Definitions:

Klinefelter Syndrome

A genetic condition in males resulting from an extra X chromosome, characterized by physical, developmental, and sometimes reproductive differences.

Turner Syndrome

A chromosomal disorder affecting females, characterized by the partial or complete absence of an X chromosome.

Genetic Disorder

A disease or condition caused by an abnormality in an individual's DNA, which can be inherited from one's parents or result from a mutation.

Extra X Chromosome

Having an extra X chromosome refers to a genetic condition where an individual, typically male, has an additional X chromosome, leading to symptoms associated with Klinefelter syndrome.