## improper integrals, convergent or divergent? follow-up

Limits, differentiation, related rates, integration, trig integrals, etc.

### improper integrals, convergent or divergent? follow-up

In this thread, a poster said:

nona.m.nona wrote:To be convergent, an integral must have a finite value. If the value is not finite, then the integral, by definition, does not converge.

What about cases like $\lim_{a \rightarrow \infty} \int_0^a \sin x dx$?
This doesn't go to infinity but still it doesn't converge.
TomasRiker

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Joined: Mon Feb 04, 2013 1:40 pm