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Math Help - Average Value of a Function

  1. #1
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    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)
    Please Help
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  2. #2
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    (1/2) sin 2 is the correct answer. Edit: my mistake.
    Last edited by icemanfan; March 19th 2010 at 02:39 PM.
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  3. #3
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    Both answers above have a sign error.
    \int_{ - 4}^0 {\cos \left( {\frac{x}<br />
{2}} \right)dx}  = \left. {2\sin \left( {\frac{x}<br />
{2}} \right)} \right|_{x =  - 4}^{x = 0}  =  - 2\sin ( - 2) =2 \sin (2)
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