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