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Math Help - Simplification of Integral

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    Simplification of Integral

    Hello!

    Does anyone of you guys see any chance to reduce/simplify this?

    The function f is generic/unknown.

    <br />
\int_t^T{f(\tau)e^{-D\tau}d\tau}<br />

    Thanks!
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  2. #2
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    Quote Originally Posted by paolopiace View Post
    Hello!

    Does anyone of you guys see any chance to reduce/simplify this?

    The function f is generic/unknown.

    <br />
\int_t^T{f(\tau)e^{-D\tau}d\tau}<br />

    Thanks!
    It's similar to a Laplace transform. I can't think of anything that can be done with it if f is arbitrary.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    It's similar to a Laplace transform. I can't think of anything that can be done with it if f is arbitrary.

    -Dan
    In fact, depending on f, it might be impossible to do.

    Or integration by parts (perhaps even repeated) might be useful:


    <br />
\int_t^T{f(\tau)e^{-D\tau}d\tau} = \left[ -\frac{-f(\tau) \, e^{-D\tau}}{D} \right]_{t}^{T} + \frac{1}{D}\int_t^T{f ' (\tau)e^{-D\tau}d\tau}<br />
.


    The observation made by topsquark could also be useful, especially perhaps if f was periodic with period T.
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