Evaluate the Integral $\int \sqrt { 16 - x ^ { 2 } } d x$

question 296

Multiple Choice

Evaluate the integral.
- $\int \sqrt { 16 - x ^ { 2 } } d x$

• A) \(\frac { x } { 2 } \sqrt { 16 - x ^ { 2 } } + 8 \sin ^ { - 1 } \frac { x } { 4 } + C\)
• B) \(\frac { x } { 2 } \sqrt { 16 - x ^ { 2 } } + 8 \sin ^ { - 1 } \frac { x } { 16 } + C\)
• C) \(\sin ^ { - 1 } \frac { x } { 4 } + C\)
• D) \(\frac { x } { 2 } \sqrt { 16 - x ^ { 2 } } - 8 \ln \left| x + \sqrt { 16 - x ^ { 2 } } \right| + C\)

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Definitions:

Nonrivalry

A characteristic of some goods where one person's consumption does not diminish the ability of others to consume the same good.

Nonexcludability

A characteristic of certain goods or services where it is not feasible to exclude individuals from using the good or service, regardless of whether they have paid for it.

Negative Externality

A cost experienced by a third party not involved in the economic transaction, such as pollution affecting residents near a factory.

Spillover Cost

A cost incurred by someone who did not choose to incur that cost.