Solve the Problem by Integration $y = \frac { 1 } { x ^ { 3 } + 4 x ^ { 2 } + 3 x } , x = 1$

question 406

Multiple Choice

Solve the problem by integration.
-Find the first-quadrant area bounded by $y = \frac { 1 } { x ^ { 3 } + 4 x ^ { 2 } + 3 x } , x = 1$ , and $x = 4$ .

• A) \(\frac { 1 } { 6 } \ln \frac { 224 } { 125 }\)
• B) \(6 \ln \frac { 125 } { 1792 }\)
• C) \(\frac { 1 } { 3 } \ln \frac { 32 } { 49 }\)
• D) \(\frac { 1 } { 6 } \ln \frac { 125 } { 1792 }\)

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Definitions:

Variable Costs

Costs that change in proportion to the level of output in the production process.

Total Fixed Cost

The sum of all costs that remain constant regardless of the level of production or output in the short run.

Marginal Cost

The expense associated with manufacturing an extra unit of a product or service.

Variable Cost

Variable cost pertains to a cost that changes in proportion with the level of activity or volume of production in a company.