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calculus

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Consider the given function and the given interval.
f(x) = 4 sin x − 2 sin 2x, [0, π]
(a) Find the average value fave of f on the given interval.
fave =



(b) Find c such that fave = f(c). (Round your answers to three decimal places.)
c = (smaller value)
c = (larger value)

  • calculus -

    the average value of the function is
    1/(π-0) ∫(4sinx - 2sin 2x)dx from x = 0 to π
    = (1/π) [-4cosx + cos 2x] from 0 to π
    = (1/π) ( -4cosπ + cos 2π - (-4cos0 + cos0) )
    = (1/π)( 4 + 1 - (-4 + 1) )
    = (1/π)(8) = 8/π

    b) if 4sinx - 2sin 2x = 8/π
    2sinx - sin 2x = 4/π
    2sinx - 2sinxcosx = 4/π
    sinx - sinxcosx = 2/π

    nasty equation to solve, I ran it through Wolfram to get
    x or c = 1.238224 or c = 2.80812

    http://www.wolframalpha.com/input/?i=sinx+-+sinxcosx+%3D+2%2Fπ

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