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Math Help - Average value of a function

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    Average value of a function

    Find the average value fave of the function f on the given interval.

    f(x)=7\sin(10x) , [-\pi, \pi]

    My integral should look like this?

    \frac{1}{\pi-(-\pi)}\int_{-\pi}^\pi \! 7\sin(10x) \, dx

    The bottom bound is supposed to be neg pi

    so then we have

    -\frac{7}{20\pi}(\cos(10x))\bigg|_{-\pi}^\pi

    Again...lower bound is neg pi anyone know how i format that when i put a - sign next to the\pi it screws it up. Anyway, am i on the right track here?
    Last edited by mr fantastic; September 19th 2009 at 05:05 PM. Reason: Fixed latex (thanks skeeter)
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    Quote Originally Posted by mmattson07 View Post
    Find the average value fave of the function f on the given interval.

    f(x)=7\sin(10x) , [-\pi, \pi]

    My integral should look like this?

    \frac{1}{\pi-(-\pi)}\int_{-\pi}^\pi \! 7\sin(10x) \, dx

    The bottom bound is supposed to be neg pi

    so then we have

    -\frac{7}{20\pi}(\cos(10x))\bigg|_{-\pi}^\pi

    Again...lower bound is neg pi anyone know how i format that when i put a - sign next to the\pi it screws it up. Anyway, am i on the right track here?
    fixed latex

    you're on the right track ...

    but note that it's much easier to know the average value of an odd function from x = -a to x = a is zero.
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    Haha wow thanks man i didnt even realize so because its the sign function right
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