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Old 2009-07-19, 22:36   #1
flouran's Avatar
Dec 2008

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Question Integral Variation

I was looking at an integral the other day:
\int_2^{x^{1/3}}\frac{dt}{\log^3 t}.
And I was told that it varies as 1.5x/log x, because I was trying to show that:
\frac{cx^{1/3}}{\log^3 x} \sim \frac{c}{\alpha}\int_2^{x^{1/3}}\frac{dt}{\log^3 t}, where \alpha can be taken as 27.
I mean, I've taken BC Calc two years ago, I took Linear Algebra last year, and I will take Differential Equations in the coming fall, but I have never heard of the term "vary" when dealing with integrals, or perhaps I know of a term with a similar definition.
Would anyone mind explaining to me what it means that the integral varies as 1.5x/log x? (and/or give me a useful link talking about it).
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