# Thread:

1. ## 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!

2. Originally Posted by paolopiace
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

3. Originally Posted by topsquark
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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