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Expert: Sherry Wallin - 12/14/2008


Question
I am having trouble solving this problem:

Find the p values for which 1/(x*ln^p(x)) is improperly integrable on interval (e, infinity)

The lower part of the fraction is x times the quantity ln to the p of x. I'm not sure if the way I typed it made sense.

Thanks

Answer
Megan~
   Hi. If you meant INT[dx/(x*(lnx)^p)] = -1/[(p-1)(lnx)^(p-1)], p not = 1, then you find for what values of p the limit
lim -1/[(p-1) (lnx)^(p-1)] is finite when x --> oo.

If p = 1 then the integral clearly diverges.
I hope this answers your question.

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Sherry Wallin

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I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

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I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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