# Thread: Average Value of a Function

1. ## Average Value of a Function

The average value of a function f(x)=cos(1/2x) on the closed interval [-4,0] is
A) -1/2 sin(2)
B) -1/4 sin (2)
C) 1/2 cos (2)
D) 1/4 sin (2)
E) 1/2 sin (2)

I don't know what I'm doing wrong but I always end up with 1/2 sin(-2)

2. (1/2) sin 2 is the correct answer. Edit: my mistake.

3. Both answers above have a sign error.
$\displaystyle \int_{ - 4}^0 {\cos \left( {\frac{x} {2}} \right)dx} = \left. {2\sin \left( {\frac{x} {2}} \right)} \right|_{x = - 4}^{x = 0} = - 2\sin ( - 2) =2 \sin (2)$