Find the Indefinite Integral $$\int x ^ { - 2 / 3 } \sqrt { x ^ { 1 / 3 } - 2 } d x$$

question 50

Multiple Choice

Find the indefinite integral.
$$\int x ^ { - 2 / 3 } \sqrt { x ^ { 1 / 3 } - 2 } d x$$

• A) \(2 \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C\)
• B) \(2 x ^ { 1 / 3 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C\)
• C) \(\frac { 1 } { 2 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C\)
• D) \(x ^ { 1 / 3 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C\)

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Definitions:

Marginal Revenue Product

The increased earnings resulting from the utilization of one more production factor unit.

Profit-maximizing

The process of adjusting the production and sale of goods and services to achieve the highest possible profit.

Marginal Product

The additional output gained by adding one more unit of a specific input, holding all other inputs constant.

Marginal Revenue Product

The additional revenue generated from employing one more unit of a resource, such as labor or capital.