Use Integration by Parts to Establish a Reduction Formula for the Integral

question 8

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \sin ^ { n } x d x$$

• A) \(\int \sin ^ { n } x d x = \sin ^ { n - 1 } x \cos x + ( n - 1 ) \int \sin ^ { n - 2 } x d x\)
• B) \(\int \sin ^ { n } x d x = - \frac { 1 } { n } \sin ^ { n - 1 } x \cos x + \frac { n - 1 } { n } \int \sin ^ { n - 2 } x d x\)
• C) \(\int \sin ^ { n } x d x = - \frac { 1 } { n } \sin ^ { n - 1 } x \cos x - \frac { n - 1 } { n } \int \sin ^ { n - 1 } x d x\)
• D) \(\int \sin ^ { n } x d x = \sin ^ { n - 1 } x \cos x - ( n - 1 ) \int \cos x \sin ^ { n - 2 } x d x\)

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A statistical test hypothesis that specifies the direction of the expected difference or relationship.