Thread: Integral Variation View Single Post
 2009-07-19, 22:36 #1 flouran     Dec 2008 72×17 Posts 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).