Use Reduction Formulas to Evaluate the Integral $\int \sin ^ { 5 } 3 x d x$

question 45

Multiple Choice

Use reduction formulas to evaluate the integral.
- $\int \sin ^ { 5 } 3 x d x$

• A) \(- \frac { 1 } { 15 } \sin ^ { 4 } 3 x \cos 3 x - \frac { 4 } { 45 } \sin ^ { 2 } 3 x \cos 3 x - \frac { 8 } { 45 } \cos 3 x + C\)
• B) \(- \frac { 1 } { 15 } \cos ^ { 4 } 3 x \sin 3 x - \frac { 8 } { 45 } \cos ^ { 2 } 3 x \sin 3 x - \frac { 2 } { 45 } \cos 3 x + C\)
• C) \(- \frac { 1 } { 15 } \sin ^ { 4 } 3 x \cos 3 x - \frac { 4 } { 45 } \sin ^ { 2 } 3 x \cos 3 x - \frac { 2 } { 9 } \sin 6 x + \frac { x } { 2 } + C\)
• D) \(- \frac { 1 } { 5 } \sin ^ { 4 } 3 x \cos 3 x - \frac { 4 } { 15 } \sin ^ { 2 } 3 x \cos 3 x - \frac { 2 } { 3 } \cos 3 x + C\)

Grasp the concept and significance of equitable remedies in the legal system.

Understand the doctrine of stare decisis and its impact on legal consistency and predictability.

Acknowledge the differentiation between civil law and criminal law in terms of legal liability.

Recognize the importance of legislative purpose in statutory interpretation and the tools used by courts to resolve ambiguities.

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