Evaluate the Integral by Using a Substitution Prior to Integration $$\int x ^ { 2 } \sqrt { x + 17 } d x$$

question 62

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int x ^ { 2 } \sqrt { x + 17 } d x$$

• A) \(\frac { \left( 30 x ^ { 2 } - 408 x + 4624 \right) ( x + 17 ) ^ { 3 / 2 } } { 105 } + C\)
• B) \(\frac { \left( 30 x ^ { 2 } - 408 x + 272 \right) ( x + 17 ) ^ { 3 / 2 } } { 105 } + C\)
• C) \(\frac { \left( 15 x ^ { 2 } - 204 x + 2312 \right) ( x + 17 ) ^ { 3 / 2 } } { 105 } + C\)
• D) \(\frac { \left( 30 x ^ { 2 } - 408 x + 4624 \right) \sqrt { ( x + 17 ) } } { 105 } + C\)

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Definitions:

Consumer Surplus

The discrepancy showcasing the difference between the sum consumers are eager to pay and the price eventually paid.

Monopolist

A single seller in a market who has significant control over the price and supply of a good or service, facing little to no competition.

Marginal Cost

The increase in cost incurred by producing one additional unit of a product or service.

Producer Surplus

The difference between what producers are willing to sell a good for and the actual market price they receive, representing a measure of producer welfare.