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Sheila
Sheila asked in Science & MathematicsMathematics · 6 years ago

The average value of f(x) = cos (1/2x) on the closed interval [-4,0] is:?

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  • Rogue
    Lv 7
    6 years ago

    ƒ[ave] = 1/(b − a) ∫[a,b] ƒ(x) dx

    ∴ ƒ[ave] = 1/(0 − -4) ∫[-4,0] cos (1/2x) dx

    ∴ ƒ[ave] = 1/4 *2sin(2)

    ∴ ƒ[ave] = sin(2)/2

    ∴ ƒ[ave] ≈ 0.45465 (5 dp)

    Source(s): http://tutorial.math.lamar.edu/Classes/CalcI/AvgFc...
  • Captain Matticus, LandPiratesInc
    Lv 7
    6 years ago

    Is that cos(x/2)?

    f(x) = cos(x/2)

    F(x) = 2 * sin(x/2)

    (F(0) - F(-4)) / (0 - (-4)) =>

    (2sin(0/2) - 2sin(-4/2)) / (4) =>

    2 * (sin(0) - sin(-2)) / 4 =>

    2 * (0 + sin(2)) / 4 =>

    sin(2) / 2

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