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

question 30

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:

Average Total Cost

The total cost of producing a certain quantity of output divided by that quantity, representing the per-unit cost of production.

Economic Losses

Financial losses incurred due to factors such as market fluctuations, business operation inefficiencies, or external events affecting the economy.

Average Variable Cost

The total variable costs (costs that change with the level of output) divided by the quantity of output produced.

Marginal Revenue

The additional income gained from selling one more unit of a good or service.