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Mean value theorem for integrals.

  1. Oct 13, 2006 #1
    find c such that (f)average=f(c)

    f(x)=7sin(x)-sin(2x), [0,pi]

    ok so i found (f)average= 14/pi

    then i tried to compute:
    7sin(c)-sin(2c)= (14/pi)

    but the answers i got were wrong.
    please if someone could reply with some helpful information on how to solve this. thank you
  2. jcsd
  3. Oct 13, 2006 #2
    this is how i would start it:

    [tex] 7\sin c - \sin 2c = \frac{14}{\pi} [/tex]

    [tex] 7\sin c - 2\sin c \cos c = \frac{14}{\pi} [/tex].

    Let [tex] a = \sin c [/tex] and [tex] b = \cos c [/tex].

    Then [tex] 7a-2ab = \frac{14}{\pi} [/tex]. We also know that [tex] a^{2} + b^{2} = 1 [/tex]. Can you go from there?
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