Use Reduction Formulas to Evaluate the Integral $\int 3 \cos ^ { 3 } x \sin ^ { 6 } x d x$

question 240

Multiple Choice

Use reduction formulas to evaluate the integral.
- $\int 3 \cos ^ { 3 } x \sin ^ { 6 } x d x$

• A) \(\frac { 3 } { 7 } \left( \sin ^ { 7 } x - \sin ^ { 9 } x \right) + C\)
• B) \(\frac { 3 } { 5 } \cos ^ { 5 } x - \frac { 3 } { 7 } \cos ^ { 7 } x + C\)
• C) \(\frac { 3 } { 7 } \sin ^ { 7 } x - \frac { 1 } { 3 } \sin ^ { 9 } x + C\)
• D) \(\frac { 3 } { 5 } \sin ^ { 5 } x - \frac { 1 } { 3 } \cos ^ { 9 } x + C\)

---

Definitions:

Failure Analysis

The systematic examination of failed components or systems to determine the underlying causes of failure and prevent future occurrences.

Developing Resilience

The process of building the capacity to recover quickly from difficulties or adapt in the face of adversity.

Resilience Training

Educational programs or strategies aimed at improving individuals' ability to withstand and recover from adverse situations, stress, or challenges.

Mental Attitudes

The psychological state of mind or disposition towards certain ideas, objects, or people, which influences behavior and perception.