Simplification of Integral

**paolopiace** · March 28th 2008, 09:01 AM

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!

**topsquark** · March 28th 2008, 10:12 AM

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

**mr fantastic** · March 28th 2008, 04:58 PM

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.

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