Converging integrals

**matty888** · April 29th 2008, 08:46 AM

Define what is meant by saying that the integral

converges.

**topsquark** · April 29th 2008, 09:03 AM

Originally Posted by matty888

Define what is meant by saying that the integral

converges.

That means it has a finite value. (Note: I am considering 0 to be a finite value. Some don't.)

-Dan

**Opalg** · April 29th 2008, 11:58 AM

It means that both of the limits $\lim_{X\to\infty}\int_{-X}^0f(x)dx$ and $\lim_{X\to\infty}\int_0^X\!\!f(x)dx$ exist (and then $\int_{-\infty}^{\infty}f(x)dx$ is defined to be the sum of those limits).

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