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) \(\tan ^ { - 1 } 5 - \tan ^ { - 1 } 4\)

Analyze the economic transitions affecting African American workers and communities.

Assess the significance of African American political participation and representation.

Acknowledge the cultural contributions of African Americans in literature, art, and entertainment.

Understand efforts, policies, and initiatives aimed at addressing racial inequalities.

---

Definitions:

Display

The act of showing or presenting something, typically for viewing by others; in social science, it can refer to behaviors or artifacts that convey social status or identity.

Ethnic Identity

The aspect of individuals' self-concept derived from membership in a group that has a common national or cultural tradition.

Symbolic Ethnicity

A form of ethnicity where attachment to one's heritage is expressed symbolically or ceremonially without deep cultural practices.

Special Occasions

Events or times that are significant or celebrated due to their cultural, religious, or personal importance.