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Old 2009-07-20, 06:52   #2
cheesehead
 
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"Richard B. Woods"
Aug 2002
Wisconsin USA

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The variable {t} is inside the integral. The variable {x} is outside the integral.

Let

{f(x)} = \int_2^{x^{1/3}}\frac{dt}{\log^3 t}.

The claim is that

{f(x)} varies as 1.5x/log x.

Quote:
Originally Posted by flouran View Post
I have never heard of the term "vary" when dealing with integrals, or perhaps I know of a term with a similar definition.
What's "varying" is the function {f(x)}.

{f(x)} happens to have an integral inside it, but that's not important for "varies".

The function varies. The function has an integral inside it. Those are two separate statements. Combining them into "the integral varies" is just a contraction that happens to be okay because the function has only the integral in it (no other terms), so referring to the function as "the integral" is permissible here.

If the function were the sum of two different integrals (presumably both with an upper limit related to x), then one would need to say, "the sum of integrals varies as ..."

Last fiddled with by cheesehead on 2009-07-20 at 07:02
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