Find the Average Value of the Function $f ( x )$

question 1

Multiple Choice

Find the average value of the function $f ( x )$ in the interval $[ - \pi , \pi ]$ .
$$f ( x ) = \sin ^ { 6 } x \cos ^ { 5 } x$$

• A) \(\pi\)
• B) 0
• C) \(\frac { \pi } { 5 }\)
• D) \(\frac { \pi } { 12 }\)
• E) \(\frac { \pi } { 6 }\)

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Definitions:

Neuroticism

A personality trait characterized by sadness, moodiness, and emotional instability.

Extroversion

A personality trait typified by outgoingness, high energy, and a preference for social interaction.

Phrenologist

A practitioner of phrenology, a now-discredited study and theory which posited that the bumps on the skull could predict mental traits and character.

Personality

The combination of characteristics or qualities that form an individual's distinctive character.