Find the Volume of the Resulting Solid If the Region $$y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$$

question 13

Short Answer

Find the volume of the resulting solid if the region under the curve
$$y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$$
from $x = 0$ to $x = 1$ is rotated about the $x$ -axis. Round your answer to four decimal places.

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Definitions:

Latency Stage

A psychoanalytic term for a period in child development from about age five to puberty during which sexual urges are inactive.

Biological Drives

Innate impulses in living organisms that prompt certain behaviors essential for survival, such as hunger, thirst, and reproduction.

Unconscious

The part of the mind that is inaccessible to the conscious mind but that affects behavior and emotions.

Id

In psychoanalytic theory, the part of the personality that is the source of instinctual impulses and demands immediate satisfaction.