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larisa [96]
3 years ago
8

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

Mathematics
1 answer:
Temka [501]3 years ago
7 0

Answer:

It diverges.

Step-by-step explanation:

We are given the inetegral:  \int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx

\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx=\int\limits^{\infty}_2 (\ln x)^2 d(\ln x)=\\\\=\lim_{t \to \infty} \int\limits^t_2 (\ln x)^2d(\ln x)=\lim_{t \to \infty} \frac{(\ln t)^3}{3} |^t_2=\infty-\frac{(\ln 2)^3}{3} =\infty

So it is divergent.

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