1. ## Simplification of Integral

Hello!

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

The function f is generic/unknown.

$
\int_t^T{f(\tau)e^{-D\tau}d\tau}
$

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.

$
\int_t^T{f(\tau)e^{-D\tau}d\tau}
$

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:

$
\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}
$
.

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