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Thread: how to solve ?

  1. December 11th 2008, 11:46 AM #1
    maobadi
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    how to solve ?

    find the mean value of y = |cosx| in the range of -Pi less than or equal to x less than or equal to Pi
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  2. December 11th 2008, 02:47 PM #2
    skeeter
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    \bar{y} = \frac{1}{\pi - (-\pi)} \int_{-\pi}^{\pi} |\cos{x}| dx

    using symmetry ...

    \bar{y} = \frac{1}{\pi} \int_{0}^{\pi} |\cos{x}| dx = \frac{1}{\pi}\left[ \int_{0}^{\frac{\pi}{2}} \cos{x} \, dx - \int_{\frac{\pi}{2}}^{\pi} \cos{x} \, dx\right]
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