The variable
is inside the integral. The variable
is outside the integral.
Let
.
The claim is that
varies as 1.5x/log x.
Quote:
Originally Posted by flouran
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
.
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 ..."