Evaluate the Integral $$\int _ { 0 } ^ { 1 / 2 } \frac { 4 d r } { \sqrt { 1 - r ^ { 2 } } }$$

question 111

Multiple Choice

Evaluate the integral.
$$\int _ { 0 } ^ { 1 / 2 } \frac { 4 d r } { \sqrt { 1 - r ^ { 2 } } }$$ Select the correct answer.

• A) \(\frac { \pi } { 4 }\)
• B) \(\frac { 1 } { 5 }\)
• C) \(\frac { \pi } { 5 }\)
• D) \(\frac { 1 } { 4 }\)
• E) \(\frac { 2 \pi } { 3 }\)

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Definitions:

Inefficiency

The lack of optimal use of resources, resulting in lost potential output or increased costs.

Monopoly Pricing

Pricing strategies employed by a monopoly, where a single firm controls the entire market for a good or service and can influence prices.

Deadweight Loss

Economic inefficiency resulting when the market equilibrium for a good or a service is not achieved.

Social Cost

The total cost to society, including both private costs and any external costs, from producing or consuming a good or service.