Integrate the Function $\int \frac { \left( 4 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$

question 252

Multiple Choice

Integrate the function.
- $\int \frac { \left( 4 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$

• A)\( - \frac { \left( 4 - t ^ { 2 } \right) ^ { 5 / 2 } } { 20 t ^ { 7 } }\)
• B) \(- \frac { 1 } { 5 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)
• C)\( - \frac { 1 } { 20 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + \sec ^ { - 1 } \left( \frac { t } { 2 } \right) + C\)
• D) \(- \frac { 1 } { 20 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)

---

Definitions:

Empathize

The ability to understand and share the feelings of another, crucial in building meaningful connections and addressing user needs.

Moment of Insight

A sudden realization or understanding of a problem's solution, often characterized by an abrupt and clear comprehension.

Bicycle Helmets

Protective headgear designed specifically to reduce the risk of head injury while cycling.

Safety-Related Reasons

Justifications or motives regarding the prevention of harm, injury, or any adverse conditions for individuals or groups.