Integrate the Function $$\int _ { 0 } ^ { 4 } \frac { 81 d x } { \left( 81 - x ^ { 2 } \right) ^ { 3 / 2 } }$$

question 92

Multiple Choice

Integrate the function.
- $$\int _ { 0 } ^ { 4 } \frac { 81 d x } { \left( 81 - x ^ { 2 } \right) ^ { 3 / 2 } }$$

• A) \(65 ^ { 3 / 2 }\)
• B) \(\sqrt { 65 } - 65\)
• C) \(\frac { 4 \sqrt { 65 } } { 65 }\)
• D) \(\frac { \sqrt { 65 } } { 65 }\)

---

Definitions:

Long Run

A period of time during which all factors of production and costs are variable, in contrast to the short run where some costs are fixed.

Short Run

A time period in economics where at least one input is fixed, affecting production capacity.

ATC

Average Total Cost refers to the total cost of production divided by the quantity of output produced.

MC

Short for Marginal Cost, it refers to the additional cost incurred by producing one more unit of a product or service.