Use Long Division to Evaluate the Integral $$\int \frac { x ^ { 2 } } { x + 7 } d x$$

question 48

Multiple Choice

Use long division to evaluate the integral.
$$\int \frac { x ^ { 2 } } { x + 7 } d x$$

• A) \(\frac { 1 } { 2 } ( x - 21 ) ( x + 7 ) + 49 \ln | x + 7 | + C\)
• B) \(\frac { 1 } { 2 } ( x + 21 ) ( x + 7 ) - 49 \ln | x + 7 | + C\)
• C) \(\frac { x ^ { 2 } } { 2 } - 14 x - 147 + \ln | x + 7 | + C\)
• D) \(\frac { x ^ { 2 } } { 2 } - 14 x + 147 + 49 \ln | x + 7 | + C\)
• E) \(\frac { x ^ { 2 } } { 2 } + 2 x + \ln | x + 49 | + C\)

Analyze how indifference curves represent consumer preferences and how their shape reflects underlying assumptions about marginal rates of substitution.

Understand the concept of a budget constraint and how it represents the trade-offs consumers face given their income and prices of goods.

Recognize the significance of behavioral economics in challenging traditional assumptions about consumer rationality.

Comprehend the principle and implications of transitivity in consumer preference rankings.

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Definitions:

Distribution Centre

A specialized facility that is responsible for receiving, storing, and distributing products to retailers or customers.

Labour Cost

The expense associated with the work performed by employees, encompassing salaries, wages, and additional benefits.

Productivity

The ratio of outputs (goods and services) divided by one or more inputs (such as labour, capital, or management).

Labour Cost Per Unit

The total expense of labor required to produce a single unit of output, encompassing wages, benefits, and any other compensation.