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:

Visible Spectrum

The portion of the electromagnetic spectrum that is visible to the human eye, typically encompassing wavelengths from about 380 to 740 nanometers.

Wave

A disturbance that transfers energy from one place to another without transferring matter.

Particle

A small localized object which can be ascribed several physical properties such as volume or mass.

Iris

The iris is the colored part of the eye that controls the diameter and size of the pupil, thus regulating the amount of light that enters the eye.