Recall That the Average of a Function $f ( x )$

Multiple Choice

Recall that the average of a function $f ( x )$ on an interval $[ a , b ]$ is $\bar { f } = \frac { 1 } { b - a } \int _ { a } ^ { b } f ( x ) \mathrm { d } x$
Calculate the 9-unit moving average of the function.
$f ( x ) = \cos \left( \frac { \pi x } { 18 } \right)$

A) $\bar { f } ( x ) = \frac { 2 } { \pi } \left( \sin \left( \frac { \pi x } { 18 } \right) - \cos \left( \frac { \pi x } { 18 } \right) \right)$
B) $\bar { f } ( x ) = \frac { 2 } { \pi } \left( \sin \left( \frac { \pi x } { 18 } \right) - \cos \left( \frac { \pi x } { 3 } \right) \right)$
C) $\bar { f } ( x ) = \frac { 2 } { \pi } \left( \sin \left( \frac { \pi x } { 18 } \right) + \cos \left( \frac { \pi x } { 2 } \right) \right)$
D) $\bar { f } ( x ) = \frac { 2 } { \pi } \left( \cos \left( \frac { \pi x } { 18 } \right) - \sin \left( \frac { \pi x } { 18 } \right) \right)$
E) $\bar { f } ( x ) = \frac { 2 } { \pi } \left( \sin \left( \frac { \pi x } { 18 } \right) + \cos \left( \frac { \pi x } { 18 } \right) \right)$