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) \(\frac { \left( 30 x ^ { 2 } - 408 x + 4624 \right) \sqrt { ( x + 17 ) } } { 105 } + C\)

Comprehend the procedures and significance of replication and meta-analysis in psychological research.

Understand the applications and implications of research findings across different cultures and the importance of cross-cultural replication for external validity.

Recognize the ethical obligations researchers have towards participants when conducting experiments, especially concerning sensitive information.

Grasp the importance of ensuring participant privacy and how information is recorded and distributed.

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Definitions:

AVC

Average Variable Cost, which is the variable cost per unit of output, calculated by dividing total variable costs by the quantity of output.

ATC

Average Total Costs, which is the sum of all production costs (fixed and variable) divided by the quantity of output produced, detailing the average cost per unit of output.

Economic Conditions

The state of an economy at a given time, encompassing factors such as inflation, unemployment rates, and GDP growth.

Decreasing-Cost Industry

An industry where average costs of production decrease as the industry grows and output increases, due to factors like technology improvements or economies of scale.