Evaluate the Integral by Using a Substitution Prior to Integration $$\int \frac { 1 } { 2 } \mathrm { e }^{ \sqrt { 7 x + 8 }}\mathrm { dx }$$

question 378

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int \frac { 1 } { 2 } \mathrm { e }^{ \sqrt { 7 x + 8 }}\mathrm { dx }$$

• A) \(( 7 x + 8 ) e^{ \sqrt { 7 x + 8 } }+ C\)
• B) \(\frac { 1 } { 7 } \mathrm { e }^{ \sqrt { 7 x + 8 }} [ \sqrt { 7 x + 8 } - 7 ] + C\)
• C) \(\frac { \sqrt { 7 x + 8 } } { 7 }\mathrm { e }^{ \sqrt { 7 x + 8 } }+ C\)
• D) \(\frac { 1 } { 7 } e^{ \sqrt { 7 x + 8 } }[ \sqrt { 7 x + 8 } - 1 ] + C\)

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Definitions:

Equilibrium

A state in which market supply and demand balance each other, and as a result, prices become stable.

Hawk-Dove Game

A model in game theory illustrating the conflict between aggressive (hawk) and peaceful (dove) strategies.

Payoff

A payoff refers to the return or the outcome received from a particular investment or decision, often evaluated in terms of profit or loss.

Proportion

A mathematical relation between parts, quantities, or amounts that expresses how much one is relative to the other.