To Three Decimal Places $\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 10.728$

question 97

Multiple Choice

$$\text { Evaluate the integral } \int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \text { using the integration limits. Round your answer }$$ to three decimal places.

• A) \(\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 10.728\)
• B) \(\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 5.272\)
• C) \(\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 9\)
• D) \(\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 9.392\)
• E) \(\int _ { 0 } ^ { 3 } \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 9 } } d x \approx 7.608\)

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Definitions:

Marginal Revenue Product

The additional revenue generated from employing one more unit of a factor of production, holding all other inputs constant.

Variable Input

An input in the production process that changes in quantity with the level of output, such as raw materials or labor hours.

Wage

The fixed regular payment, typically calculated on an hourly, daily, or piecework basis, made by an employer to an employee.

Marginal Product

The additional output that is produced by adding one more unit of a specific input, keeping all other inputs constant.