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Math Help - average value on an interval

  1. #1
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    Question average value on an interval

    please help!

    The average value of cosx on the interval [-3,5] is...?

    I looked in my book and asked a friend but nobody understands...the answer is supposed to be (sin3 + sin5)/8...
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  2. #2
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    Quote Originally Posted by abcocoa View Post
    please help!

    The average value of cosx on the interval [-3,5] is...?

    I looked in my book and asked a friend but nobody understands...the answer is supposed to be (sin3 + sin5)/8...
    \int_{-3}^5 \cos x=\sin x\big|_{-3}^5=\sin5-\sin(-3)=\sin 5+\sin 8
    Then divide it by the length of interval,
    5-(-3)=8
    Correct answer thou hath.
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  3. #3
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    In general (assuming the integral can be done, etc.) the average (mean) value of a function f(x) over the interval (a, b) is:
    \overline{f} = \frac{1}{b - a} \int_a^b dx f(x)

    You can find this under the heading "mean value theorem for integration" or something similar.

    -Dan
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