Should You Add dy to the Line Integral Expression?

[-Vitaly-]

Homework Statement

Hello, I'm writing a summary of all calculus I've learned during this term and now I'm on line integrals. I wrote this so far:
http://img17.imageshack.us/img17/9776/algebrac.jpg
But I have Sigma of x and y (a similar expression was in my lecture notes), but there is no dy anywhere, do I need to add dy to that expression? or just treat y as a constant? (if line density is given as a function of x and y)

Homework Equations

The Attempt at a Solution

 

[Galileo]

There is no real y-dependence. Remember that the shape of the chain is given as some function of x. So, given x, what should y be?

 

[-Vitaly-]

There is no real y-dependence. Remember that the shape of the chain is given as some function of x. So, given x, what should y be?

Oh, so just rearrange y in terms of x :D Thanks