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anonymous
 4 years ago
I really need help on improper integrals, please respond?
anonymous
 4 years ago
I really need help on improper integrals, please respond?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, so I'm really confused as to what to do. Let's do an example problem, \[\int\limits_{0}^{1} dx/3x2\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0this isn't an improper integral

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's dx over 3x2, i'm looking at my book right now.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay. so I don't know what to do.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well 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".

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0We need to split this integral

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{2/3}\frac{dx}{3x2}+\int\limits_{2/3}^{1}\frac{dx}{3x2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do you know what to do next?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0We evaluate the onesided limits of each term separately:\[\int\limits_{0}^{2/3}\frac{dx}{3x2}=\lim_{t \rightarrow 2/3^{1}}\int\limits_{0}^{t}\frac{dx}{3x2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I get:\[\lim_{t \rightarrow (2/3)^{1}}\frac{1}{3}(\ln \left 3t2 \right\ln \left 02 \right)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'll let you take it from here

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes, it diverges so you wouldn't continue. Therefore the answer you just be that.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dont forget to medal me to close this question
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