Hi all.(adsbygoogle = window.adsbygoogle || []).push({});

Sorry about creating this new threat despite existing some others on the same topic.

I have a problem in understanding a very specific step in the mentioned proof.

Let me take the proof given in this link as our guide.

My problem is just at the ending. When it says:

"The region of integration for this last iterated integral is the wedge-shaped region in the (t, τ) plane shown in Figure 12.28. We reverse the order of integration in the integral to get:"

$$F(s)G(s) = \int_0^\infty \left[ \int_0^t f(t)·g(\tau-t)·e^{-st}\; \mathrm{d}\tau\right]\; \mathrm{d}t$$

I don't understand how this reversion gives these limits of integration. How do we get from

$$F(s)G(s) = \int_0^\infty \left[ \int_\tau^\infty f(t)·g(\tau-t)·e^{-st}\; \mathrm{d}t\right]\; \mathrm{d}\tau$$

to there?

Thanks.

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# Convolution theorem for Laplace Transform proof

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