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Determine whether the improper integral converges or diverges, and find the value of each that converges.

∫^-1_-[infinity] ln |x| dx

1 Answer

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Answer:

It diverges.

Explanation:

We are given the integral:
\int\limits^(-1)_(-\infty) \ln |x| dx


\int\limits^(-1)_(-\infty) \ln |x| dx=\int\limits^(-1)_(-\infty) \ln (-x) dx=\\\\= \lim_(t \to \infty) \int\limits^(-1)_(-t) \ln (-x) dx= \lim_(t \to \infty)( x(\ln \left(-x\right)-1))|^(-1)_(-t)=1-\infty=-\infty

So it is divergent.

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