Use a Trigonometric Substitution to Evaluate the Integral $$\int _ { 0 } ^ { 5 } \frac { 4 e ^ { - t } } { 1 + 16 e ^ { - 2 t } } d t$$

question 318

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int _ { 0 } ^ { 5 } \frac { 4 e ^ { - t } } { 1 + 16 e ^ { - 2 t } } d t$$

• A) \(\tan ^ { - 1 } \frac { 4 } { e ^ { 5 } } - \tan ^ { - 1 } 4\)
• B) \(\tan ^ { - 1 } 4 - \tan ^ { - 1 } \frac { 4 } { e ^ { 5 } }\)
• C) \(\frac { 1 } { 4 } \tan ^ { - 1 } 4 - \frac { 1 } { 4 } \tan ^ { - 1 } \frac { 4 } { e ^ { 5 } }\)
• D) \(\tan ^ { - 1 } 5 - \tan ^ { - 1 } 4\)

Understand different types of conflicts and how they manifest in real-life situations.

Recognize psychological responses to stress and conflict, including coping mechanisms and emotional reactions.

Identify the role of physiological reactions in the fight-or-flight response.

Comprehend the impact of stress on performance, including the concept of optimal arousal.

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