# Line integrals in physics

Wasn't sure which section to put this q in.

Just reading now that f(x,y) can represent the density of a semicircular wire and so if you take a line integral of some curve C and f(x,y) you can find the mass of the wire... makes sense.

What I don't get is that if I then move the wire around the xy axis it's mass will change. What am I missing?

f(x,y) gives you a value of density for all points in the x-y plane. Taking a line integral through that plane is like 'cutting out' a wire from that density plane.

Unless f(x,y) is constant, there is no reason to assume that one wire cut out would be the same density as another.

I think what you're not realizing is that the weight isn't linked to C.

How is weight not linked to C? to find weight/mass you must take a line integral through that plane, and that line integral is C.

What I was confused about is if I take a 3cm wire and position it from (0,0) to (0,3) and then I move it to some other place in the xy plane suddenly it's weight should change right? which is what doesn't make sense to me...

WannabeNewton