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Alona [7]
3 years ago
5

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

Mathematics
1 answer:
pantera1 [17]3 years ago
7 0

Answer:

It diverges.

Step-by-step 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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