I really need help on improper integrals, please respond?

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I really need help on improper integrals, please respond?

Mathematics
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ok
Okay, so I'm really confused as to what to do. Let's do an example problem, \[\int\limits_{0}^{1} dx/3x-2\]
this isn't an improper integral

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It's dx over 3x-2, i'm looking at my book right now.
ok
okay. so I don't know what to do.
well we can't have a zero denominator, which means we can't have x=2/3. This lies within our limits of integration which is why the integral is "improper".
We need to split this integral
what are the steps?
\[\int\limits_{0}^{2/3}\frac{dx}{3x-2}+\int\limits_{2/3}^{1}\frac{dx}{3x-2}\]
do you know what to do next?
We evaluate the one-sided limits of each term separately:\[\int\limits_{0}^{2/3}\frac{dx}{3x-2}=\lim_{t \rightarrow 2/3^{-1}}\int\limits_{0}^{t}\frac{dx}{3x-2}\]
I get:\[\lim_{t \rightarrow (2/3)^{-1}}\frac{1}{3}(\ln \left| 3t-2 \right|-\ln \left| 0-2 \right|)\]
I'll let you take it from here
Yes, it diverges so you wouldn't continue. Therefore the answer you just be that.
yeppers
dont forget to medal me to close this question

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