Evaluate the Integral in Terms of Natural Logarithms $$\int _ { 4 } ^ { 7 } \frac { d x } { \sqrt { x ^ { 2 } - 9 } }$$

question 77

Multiple Choice

Evaluate the integral in terms of natural logarithms.
- $$\int _ { 4 } ^ { 7 } \frac { d x } { \sqrt { x ^ { 2 } - 9 } }$$

• A) \(\ln \left( \frac { 7 + \sqrt { 40 } } { 23 } \right) - 1\)
• B) \(\frac { 1 } { 2 } \ln \left( \frac { \sqrt { 40 } } { 4 + \sqrt { 7 } } \right)\)
• C) \(\ln 4\)
• D) \(\ln \left( \frac { 7 + \sqrt { 40 } } { 4 + \sqrt { 7 } } \right)\)

Learn the critical difference between marginal revenue vs. marginal cost, and their importance in computing a firm's total profit.

Analyze the role of explicit and implicit costs in different professional contexts to comprehend their impact on total costs and profits.

Learn about cost behavior, including variable, fixed, and marginal costs, and their relationship to output production.

Understand how the production function influences cost curves and the significance of marginal product.

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Definitions:

Marginal Cost

The rise in expense incurred from manufacturing an extra unit of a product or service.

Shutdown Point

The level of operations at which a company does not benefit from continuing operations or producing any output due to high variable costs.

Output

The total amount of goods or services produced by an economic system or entity within a given period.

Peak Efficiency

Refers to the highest level of operational productivity or performance a company or economy can achieve under ideal conditions.