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

question 16

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:

Upward Sloping

A term often used in economics to describe a curve or line that increases in height as it moves from left to right, indicative of a positive relationship between two variables.

Compact Disc

A physical medium for the storage and playback of digital audio and data, utilizing laser technology for reading and writing information.

Average Costs

Calculated by dividing the total cost of production by the quantity of output produced, indicating the cost per unit of output.

Output Increases

A rise in the quantity of goods or services produced by a firm or economy.